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Fp(The)f(Y)l (etter-Drinfel'd)j(mo)n(dule)e(of)f(derivations)0 2608 y Fr(Der)s Fz(\()p Fy(A)p Fz(\))17 b Fp(of)h(an)f(algebr)n(a)h Fy(A)f Fp(is)h(a)f(Lie)g(algebr)n(a.)p eop %%Page: 17 17 17 16 bop 67 125 a Fu(SKEW-PRIMITIVE)17 b(ELEMENTS)g(OF)f(QUANTUM)g(GR) o(OUPS)h(AND)g(BRAIDED)g(LIE)g(ALGEBRAS)29 b(17)50 225 y Fz(No)o(w)12 b(let)g Fy(V)23 b Fz(b)q(e)13 b(in)f Ft(Y)t(D)467 207 y Fx(K)466 238 y(K)514 225 y Fz(with)g(inner)g(endomorphism)e(ob)s (ject)i Fy(A)i Fz(:=)f Fr(end)r Fz(\()p Fy(V)e Fz(\).)20 b(Giv)o(en)11 b(a)i(bilin-)0 283 y(ear)h(form)e Ft(h)p Fy(:;)c(:)p Ft(i)14 b Fz(:)f Fy(V)k Ft(\012)6 b Fy(V)24 b Ft(\000)-30 b(!)14 b Fy(k)h Fz(in)e Ft(Y)t(D)705 265 y Fx(K)704 296 y(K)741 283 y Fz(.)20 b(W)l(e)13 b(collect)f(the)i(set)f Ff(g)h Fz(of)g Fp(skew-symmetric)g Fz(endomor-)0 341 y(phisms)h Fy(f)20 b Ft(2)14 b Fr(end)r Fz(\()p Fy(V)d Fz(\))17 b(for)f(whic)o(h)g(in)g(principle)f(the)h(follo)o(wing)g (hold:)22 b Ft(h)p Fy(f)5 b Fz(\()p Fy(v)r Fz(\))p Fy(;)j(w)q Ft(i)15 b Fz(=)f 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1252 V 792 1253 V 790 1255 V 787 1256 V 785 1257 V 782 1259 V 224 w(r)p 971 1212 V 971 1213 V 971 1215 V 971 1216 V 971 1218 V 972 1219 V 972 1220 V 973 1222 V 973 1223 V 974 1224 V 975 1226 V 975 1227 V 976 1228 V 977 1230 V 978 1231 V 979 1232 V 981 1234 V 982 1235 V 983 1236 V 985 1238 V 986 1239 V 988 1240 V 989 1242 V 991 1243 V 993 1244 V 995 1246 V 997 1247 V 999 1249 V 1001 1250 V 1003 1251 V 1005 1252 V 1008 1253 V 1010 1255 V 1013 1256 V 1015 1257 V 1018 1259 V 1042 1236 V 1042 1237 V 1041 1237 V 1041 1238 V 1041 1239 V 1041 1240 V 1041 1240 V 1041 1241 V 1040 1242 V 1040 1243 V 1040 1243 V 1039 1244 V 1039 1245 V 1038 1246 V 1038 1246 V 1037 1247 V 1037 1248 V 1036 1248 V 1035 1249 V 1035 1250 V 1034 1250 V 1033 1251 V 1032 1251 V 1031 1252 V 1030 1252 V 1030 1253 V 1029 1254 V 1028 1254 V 1026 1255 V 1025 1255 V 1024 1256 V 1023 1257 V 1022 1257 V 1021 1258 V 1019 1258 V 1018 1259 V 734 1211 2 48 v 781 1211 V 828 1211 V 1064 1211 V 1018 1165 2 2 v 1018 1166 V 1018 1166 V 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978 1178 V 978 1178 V 979 1179 V 980 1180 V 981 1180 V 982 1181 V 983 1182 V 984 1182 V 985 1183 V 986 1184 V 987 1184 V 988 1185 V 989 1186 V 990 1187 V 992 1187 V 993 1188 V 994 1189 V 1018 1212 V 1018 1211 V 1018 1211 V 1018 1210 V 1018 1209 V 1017 1209 V 1017 1208 V 1017 1207 V 1017 1207 V 1016 1206 V 1016 1205 V 1016 1205 V 1015 1204 V 1015 1203 V 1014 1203 V 1014 1202 V 1013 1201 V 1012 1201 V 1012 1200 V 1011 1199 V 1010 1199 V 1009 1198 V 1009 1197 V 1008 1197 V 1007 1196 V 1006 1195 V 1005 1195 V 1004 1194 V 1003 1193 V 1002 1193 V 1001 1192 V 999 1191 V 998 1191 V 997 1190 V 996 1189 V 994 1189 V 733 1218 2 7 v 733 1237 a(\006)p 780 1218 V 14 w(\005)p 751 1237 14 2 v 1016 1218 2 7 v 203 w(\006)p 1063 1218 V 14 w(\005)p 1035 1237 14 2 v 722 1150 a Ff(g)211 b(g)762 1159 y Fy(V)20 b(V)160 b(V)20 b(V)857 1207 y Fz(=)904 1202 y Ft(\000)0 1370 y FD(Theorem)12 b(6.6.)17 b Fp(F)l(or)c(a)h(Y)l(etter-Drinfel'd)i(mo)n(dule)e Fy(V)25 b Ft(2)14 b(Y)t(D)1153 1352 y Fx(K)1152 1383 y(K)1202 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b(pro)o(v)o(e)g(this)h(b)o(y)f(induction.)38 b(F)l(or)21 b Fy(n)j Fz(=)f(1)f(this)g(is)f(the)h(de\014ning)g (condition)f(for)h Ff(g)p Fz(.)38 b(The)0 2134 y(induction)16 b(step)g(is)p 144 2365 2 95 v 191 2318 2 48 v 168 2413 2 24 v 239 2365 2 95 v 286 2436 2 166 v 380 2342 2 71 v 427 2318 2 48 v 475 2365 2 95 v 522 2413 2 142 v 710 2342 2 71 v 758 2318 2 48 v 805 2365 2 95 v 852 2389 2 118 v 1135 2318 2 48 v 1182 2365 2 95 v 143 2372 2 7 v 143 2391 a Fe(\006)p 191 2372 V 15 w(\005)p 162 2391 14 2 v 167 2420 2 7 v 167 2438 a(\006)p 214 2420 V 14 w(\005)p 185 2438 14 2 v 403 2396 2 7 v 403 2414 a(\006)p 450 2396 V 14 w(\005)p 421 2414 14 2 v 426 2372 2 7 v 426 2391 a(\006)p 474 2372 V 15 w(\005)p 445 2391 14 2 v 757 2372 2 7 v 250 w(\006)p 804 2372 V 14 w(\005)p 775 2391 14 2 v 780 2443 2 7 v 780 2461 a(\006)p 828 2443 V 15 w(\005)p 799 2461 14 2 v 1040 2372 2 7 v 1040 2391 a(\006)p 1087 2372 V 14 w(\005)p 1058 2391 14 2 v 1134 2372 2 7 v 14 w(\006)p 1181 2372 V 14 w(\005)p 1153 2391 14 2 v 782 2390 2 2 v 782 2391 V 782 2391 V 782 2392 V 782 2392 V 782 2393 V 782 2394 V 781 2394 V 781 2395 V 781 2396 V 781 2396 V 781 2397 V 780 2397 V 780 2398 V 780 2399 V 779 2399 V 779 2400 V 779 2400 V 778 2401 V 778 2401 V 777 2402 V 777 2402 V 776 2403 V 776 2403 V 775 2404 V 775 2404 V 774 2405 V 774 2405 V 773 2406 V 772 2406 V 772 2407 V 771 2407 V 770 2407 V 769 2408 V 769 2408 V 768 2409 V 735 2437 V 735 2436 V 735 2436 V 735 2435 V 735 2434 V 735 2434 V 735 2433 V 735 2433 V 736 2432 V 736 2431 V 736 2431 V 736 2430 V 737 2429 V 737 2429 V 737 2428 V 737 2428 V 738 2427 V 738 2427 V 739 2426 V 739 2426 V 739 2425 V 740 2425 V 740 2424 V 741 2424 V 742 2423 V 742 2423 V 743 2422 V 743 2422 V 744 2421 V 745 2421 V 745 2420 V 746 2420 V 747 2419 V 747 2419 V 748 2419 V 749 2418 V 735 2390 V 735 2391 V 735 2391 V 735 2392 V 735 2393 V 735 2393 V 736 2394 V 736 2395 V 736 2395 V 736 2396 V 737 2397 V 737 2397 V 738 2398 V 738 2399 V 739 2399 V 739 2400 V 740 2401 V 740 2401 V 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1087 2313 V 1087 2312 V 1086 2312 V 1086 2311 V 1085 2310 V 1085 2310 V 1084 2309 V 1084 2308 V 1083 2308 V 1082 2307 V 1082 2306 V 1081 2306 V 1080 2305 V 1079 2304 V 1079 2304 V 1078 2303 V 1077 2302 V 1076 2302 V 1075 2301 V 1074 2300 V 1073 2300 V 1071 2299 V 1070 2298 V 1069 2298 V 1068 2297 V 1066 2296 V 1065 2295 V 1136 2319 V 1136 2320 V 1136 2320 V 1136 2321 V 1136 2322 V 1136 2322 V 1136 2323 V 1135 2324 V 1135 2324 V 1135 2325 V 1135 2325 V 1135 2326 V 1134 2327 V 1134 2327 V 1134 2328 V 1133 2328 V 1133 2329 V 1133 2329 V 1132 2330 V 1132 2330 V 1131 2331 V 1131 2332 V 1130 2332 V 1130 2333 V 1129 2333 V 1129 2334 V 1128 2334 V 1127 2334 V 1127 2335 V 1126 2335 V 1126 2336 V 1125 2336 V 1124 2337 V 1123 2337 V 1123 2338 V 1122 2338 V 1089 2366 V 1089 2366 V 1089 2365 V 1089 2364 V 1089 2364 V 1089 2363 V 1089 2362 V 1089 2362 V 1089 2361 V 1090 2361 V 1090 2360 V 1090 2359 V 1090 2359 V 1091 2358 V 1091 2358 V 1091 2357 V 1092 2356 V 1092 2356 V 1092 2355 V 1093 2355 V 1093 2354 V 1094 2354 V 1094 2353 V 1095 2353 V 1095 2352 V 1096 2352 V 1097 2351 V 1097 2351 V 1098 2350 V 1098 2350 V 1099 2350 V 1100 2349 V 1101 2349 V 1101 2348 V 1102 2348 V 1103 2347 V 1089 2319 V 1089 2320 V 1089 2320 V 1089 2321 V 1089 2322 V 1089 2322 V 1089 2323 V 1090 2324 V 1090 2324 V 1090 2325 V 1091 2326 V 1091 2326 V 1092 2327 V 1092 2328 V 1093 2329 V 1093 2329 V 1094 2330 V 1094 2331 V 1095 2331 V 1096 2332 V 1096 2333 V 1097 2333 V 1098 2334 V 1099 2335 V 1100 2335 V 1101 2336 V 1102 2337 V 1103 2337 V 1104 2338 V 1105 2339 V 1106 2339 V 1107 2340 V 1108 2341 V 1110 2341 V 1111 2342 V 1112 2343 V 1136 2366 V 1136 2366 V 1136 2365 V 1136 2364 V 1136 2364 V 1135 2363 V 1135 2362 V 1135 2362 V 1135 2361 V 1134 2360 V 1134 2360 V 1134 2359 V 1133 2358 V 1133 2357 V 1132 2357 V 1132 2356 V 1131 2355 V 1130 2355 V 1130 2354 V 1129 2353 V 1128 2353 V 1127 2352 V 1127 2351 V 1126 2351 V 1125 2350 V 1124 2349 V 1123 2349 V 1122 2348 V 1121 2347 V 1120 2347 V 1119 2346 V 1117 2345 V 1116 2345 V 1115 2344 V 1114 2343 V 1112 2343 V 216 2413 V 216 2413 V 216 2412 V 216 2411 V 216 2410 V 216 2409 V 216 2409 V 216 2408 V 216 2407 V 216 2406 V 217 2406 V 217 2405 V 217 2404 V 217 2404 V 217 2403 V 218 2402 V 218 2401 V 218 2401 V 218 2400 V 219 2399 V 219 2399 V 219 2398 V 220 2398 V 220 2397 V 220 2396 V 221 2396 V 221 2395 V 221 2394 V 222 2394 V 222 2393 V 223 2393 V 223 2392 V 224 2392 V 224 2391 V 225 2390 V 225 2390 V 225 2390 V 226 2389 V 227 2389 V 228 2388 V 228 2388 V 229 2387 V 230 2386 V 230 2386 V 231 2385 V 232 2385 V 232 2384 V 233 2383 V 233 2383 V 234 2382 V 234 2382 V 235 2381 V 235 2380 V 236 2380 V 236 2379 V 236 2378 V 237 2378 V 237 2377 V 237 2376 V 238 2375 V 238 2375 V 238 2374 V 238 2373 V 239 2372 V 239 2372 V 239 2371 V 239 2370 V 239 2369 V 239 2369 V 239 2368 V 239 2367 V 239 2366 V 405 2390 V 405 2389 V 405 2388 V 404 2387 V 404 2387 V 404 2386 V 404 2385 V 404 2384 V 404 2384 V 404 2383 V 404 2382 V 404 2381 V 403 2381 V 403 2380 V 403 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2404 V 849 2403 V 849 2402 V 850 2402 V 850 2401 V 851 2400 V 851 2400 V 851 2399 V 851 2398 V 852 2398 V 852 2397 V 852 2396 V 852 2395 V 852 2395 V 853 2394 V 853 2393 V 853 2392 V 853 2391 V 853 2391 V 853 2390 V 239 2483 a(r)p 192 2437 V 192 2438 V 192 2440 V 193 2441 V 193 2442 V 193 2444 V 194 2445 V 194 2446 V 195 2448 V 195 2449 V 196 2451 V 197 2452 V 198 2453 V 199 2455 V 200 2456 V 201 2457 V 202 2459 V 203 2460 V 205 2461 V 206 2463 V 208 2464 V 209 2465 V 211 2467 V 213 2468 V 214 2469 V 216 2471 V 218 2472 V 220 2473 V 222 2475 V 225 2476 V 227 2477 V 229 2479 V 232 2480 V 234 2482 V 237 2483 V 239 2484 V 287 2437 V 287 2438 V 286 2440 V 286 2441 V 286 2442 V 286 2444 V 285 2445 V 285 2446 V 284 2448 V 283 2449 V 283 2451 V 282 2452 V 281 2453 V 280 2455 V 279 2456 V 278 2457 V 277 2459 V 275 2460 V 274 2461 V 273 2463 V 271 2464 V 270 2465 V 268 2467 V 266 2468 V 264 2469 V 263 2471 V 261 2472 V 259 2473 V 256 2475 V 254 2476 V 252 2477 V 250 2479 V 247 2480 V 245 2482 V 242 2483 V 239 2484 V 475 2460 a(r)p 428 2413 V 428 2415 V 428 2416 V 429 2417 V 429 2419 V 429 2420 V 430 2422 V 430 2423 V 431 2424 V 431 2426 V 432 2427 V 433 2428 V 434 2430 V 435 2431 V 436 2432 V 437 2434 V 438 2435 V 439 2436 V 441 2438 V 442 2439 V 444 2440 V 445 2442 V 447 2443 V 449 2444 V 450 2446 V 452 2447 V 454 2448 V 456 2450 V 458 2451 V 461 2453 V 463 2454 V 465 2455 V 468 2457 V 470 2458 V 473 2459 V 475 2461 V 523 2413 V 522 2415 V 522 2416 V 522 2417 V 522 2419 V 522 2420 V 521 2422 V 521 2423 V 520 2424 V 519 2426 V 519 2427 V 518 2428 V 517 2430 V 516 2431 V 515 2432 V 514 2434 V 513 2435 V 511 2436 V 510 2438 V 509 2439 V 507 2440 V 506 2442 V 504 2443 V 502 2444 V 500 2446 V 498 2447 V 496 2448 V 494 2450 V 492 2451 V 490 2453 V 488 2454 V 486 2455 V 483 2457 V 481 2458 V 478 2459 V 475 2461 V 782 2483 a(r)p 735 2437 V 735 2438 V 735 2440 V 735 2441 V 735 2442 V 736 2444 V 736 2445 V 737 2446 V 737 2448 V 738 2449 V 739 2451 V 740 2452 V 740 2453 V 741 2455 V 742 2456 V 744 2457 V 745 2459 V 746 2460 V 747 2461 V 749 2463 V 750 2464 V 752 2465 V 753 2467 V 755 2468 V 757 2469 V 759 2471 V 761 2472 V 763 2473 V 765 2475 V 767 2476 V 770 2477 V 772 2479 V 774 2480 V 777 2482 V 779 2483 V 782 2484 V 806 2461 V 806 2461 V 806 2462 V 805 2463 V 805 2464 V 805 2465 V 805 2465 V 805 2466 V 804 2467 V 804 2468 V 804 2468 V 803 2469 V 803 2470 V 802 2470 V 802 2471 V 801 2472 V 801 2473 V 800 2473 V 799 2474 V 799 2475 V 798 2475 V 797 2476 V 796 2477 V 795 2477 V 795 2478 V 794 2478 V 793 2479 V 792 2480 V 791 2480 V 789 2481 V 788 2481 V 787 2482 V 786 2483 V 785 2483 V 783 2484 V 782 2484 V 1112 2436 a(r)p 1065 2390 V 1065 2391 V 1065 2393 V 1065 2394 V 1066 2395 V 1066 2397 V 1067 2398 V 1067 2399 V 1068 2401 V 1068 2402 V 1069 2403 V 1070 2405 V 1071 2406 V 1072 2407 V 1073 2409 V 1074 2410 V 1075 2411 V 1076 2413 V 1078 2414 V 1079 2415 V 1081 2417 V 1082 2418 V 1084 2420 V 1086 2421 V 1087 2422 V 1089 2424 V 1091 2425 V 1093 2426 V 1095 2428 V 1098 2429 V 1100 2430 V 1102 2432 V 1105 2433 V 1107 2434 V 1110 2436 V 1112 2437 V 1160 2390 V 1159 2391 V 1159 2393 V 1159 2394 V 1159 2395 V 1159 2397 V 1158 2398 V 1158 2399 V 1157 2401 V 1156 2402 V 1156 2403 V 1155 2405 V 1154 2406 V 1153 2407 V 1152 2409 V 1151 2410 V 1150 2411 V 1148 2413 V 1147 2414 V 1146 2415 V 1144 2417 V 1143 2418 V 1141 2420 V 1139 2421 V 1137 2422 V 1135 2424 V 1133 2425 V 1131 2426 V 1129 2428 V 1127 2429 V 1125 2430 V 1123 2432 V 1120 2433 V 1118 2434 V 1115 2436 V 1112 2437 V 136 2314 a Ft(r)178 2295 y Fx(n)174 2361 y Fy(A)133 2233 y Ff(g)10 b(g)193 2215 y Fx(n)220 2243 y Fy(V)19 b(V)410 2361 y(A)368 2233 y Ff(g)11 b(g)429 2215 y Fx(n)456 2243 y Fy(V)19 b(V)740 2361 y(A)699 2233 y Ff(g)10 b(g)759 2215 y Fx(n)786 2243 y Fy(V)19 b(V)1023 2361 y(A)1029 2233 y Ff(g)10 b(g)1089 2215 y Fx(n)1116 2243 y Fy(V)19 b(V)315 2384 y Fz(=)198 b(=)292 b(=)g(=)590 2381 y(\()p Ft(\000)p Fz(1\))229 b(\()p Ft(\000)p Fz(1\))p 1560 2318 2 48 v 1607 2365 2 95 v 1513 2272 2 2 v 1513 2273 V 1513 2273 V 1513 2274 V 1513 2275 V 1513 2275 V 1513 2276 V 1513 2276 V 1513 2277 V 1512 2278 V 1512 2278 V 1512 2279 V 1512 2279 V 1511 2280 V 1511 2281 V 1511 2281 V 1510 2282 V 1510 2282 V 1510 2283 V 1509 2283 V 1509 2284 V 1508 2284 V 1508 2285 V 1507 2285 V 1507 2286 V 1506 2286 V 1506 2287 V 1505 2287 V 1504 2288 V 1504 2288 V 1503 2289 V 1502 2289 V 1502 2290 V 1501 2290 V 1500 2290 V 1499 2291 V 1466 2319 V 1466 2318 V 1466 2318 V 1466 2317 V 1466 2316 V 1467 2316 V 1467 2315 V 1467 2315 V 1467 2314 V 1467 2313 V 1467 2313 V 1468 2312 V 1468 2312 V 1468 2311 V 1468 2310 V 1469 2310 V 1469 2309 V 1470 2309 V 1470 2308 V 1470 2308 V 1471 2307 V 1471 2307 V 1472 2306 V 1472 2306 V 1473 2305 V 1473 2305 V 1474 2304 V 1475 2304 V 1475 2303 V 1476 2303 V 1477 2302 V 1477 2302 V 1478 2301 V 1479 2301 V 1480 2301 V 1480 2300 V 1466 2272 V 1466 2273 V 1466 2273 V 1466 2274 V 1467 2275 V 1467 2275 V 1467 2276 V 1467 2277 V 1467 2277 V 1468 2278 V 1468 2279 V 1469 2279 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1554 2333 V 1554 2333 V 1553 2334 V 1553 2334 V 1552 2334 V 1552 2335 V 1551 2335 V 1550 2336 V 1549 2336 V 1549 2337 V 1548 2337 V 1547 2338 V 1546 2338 V 1513 2366 V 1513 2366 V 1513 2365 V 1514 2364 V 1514 2364 V 1514 2363 V 1514 2362 V 1514 2362 V 1514 2361 V 1514 2361 V 1515 2360 V 1515 2359 V 1515 2359 V 1515 2358 V 1516 2358 V 1516 2357 V 1516 2356 V 1517 2356 V 1517 2355 V 1518 2355 V 1518 2354 V 1518 2354 V 1519 2353 V 1520 2353 V 1520 2352 V 1521 2352 V 1521 2351 V 1522 2351 V 1522 2350 V 1523 2350 V 1524 2350 V 1525 2349 V 1525 2349 V 1526 2348 V 1527 2348 V 1528 2347 V 1513 2319 V 1513 2320 V 1513 2320 V 1514 2321 V 1514 2322 V 1514 2322 V 1514 2323 V 1514 2324 V 1515 2324 V 1515 2325 V 1515 2326 V 1516 2326 V 1516 2327 V 1517 2328 V 1517 2329 V 1518 2329 V 1518 2330 V 1519 2331 V 1520 2331 V 1520 2332 V 1521 2333 V 1522 2333 V 1523 2334 V 1524 2335 V 1524 2335 V 1525 2336 V 1526 2337 V 1527 2337 V 1528 2338 V 1530 2339 V 1531 2339 V 1532 2340 V 1533 2341 V 1534 2341 V 1536 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1581 2395 V 1582 2395 V 1582 2394 V 1582 2394 V 1583 2394 V 1583 2393 V 1583 2393 V 1583 2393 V 1583 2392 V 1584 2392 V 1584 2392 V 1584 2391 V 1584 2391 V 1584 2391 V 1584 2390 V 1584 2390 V 1584 2390 V 1211 2384 a Fz(=)1263 2381 y(\()p Ft(\000)p Fz(1\))1364 2363 y Fx(n)p Fq(+1)1448 2361 y Fy(A)1454 2233 y Ff(g)10 b(g)1514 2215 y Fx(n)1541 2243 y Fy(V)19 b(V)1636 2384 y Fz(=)1513 2460 y Fe(r)p 1466 2413 V 1466 2415 V 1466 2416 V 1467 2417 V 1467 2419 V 1467 2420 V 1468 2422 V 1468 2423 V 1469 2424 V 1469 2426 V 1470 2427 V 1471 2428 V 1472 2430 V 1473 2431 V 1474 2432 V 1475 2434 V 1476 2435 V 1477 2436 V 1479 2438 V 1480 2439 V 1482 2440 V 1483 2442 V 1485 2443 V 1487 2444 V 1488 2446 V 1490 2447 V 1492 2448 V 1494 2450 V 1496 2451 V 1499 2453 V 1501 2454 V 1503 2455 V 1506 2457 V 1508 2458 V 1511 2459 V 1513 2461 V 1537 2437 V 1537 2438 V 1537 2439 V 1537 2439 V 1537 2440 V 1537 2441 V 1536 2442 V 1536 2443 V 1536 2443 V 1535 2444 V 1535 2445 V 1535 2445 V 1534 2446 V 1534 2447 V 1533 2448 V 1533 2448 V 1532 2449 V 1531 2450 V 1531 2450 V 1530 2451 V 1529 2452 V 1528 2452 V 1528 2453 V 1527 2454 V 1526 2454 V 1525 2455 V 1524 2455 V 1523 2456 V 1522 2457 V 1521 2457 V 1520 2458 V 1518 2458 V 1517 2459 V 1516 2460 V 1515 2460 V 1513 2461 V eop %%Page: 18 18 18 17 bop 0 125 a Fu(18)705 b(BODO)13 b(P)m(AREIGIS)p 451 358 2 48 v 451 500 2 95 v 545 311 2 48 v 545 452 2 95 v 592 429 2 166 v 876 358 2 48 v 923 405 2 95 v 970 452 2 189 v 1017 500 2 236 v 1489 358 2 95 v 1489 500 2 48 v 1536 405 2 142 v 1583 452 2 189 v 499 265 2 2 v 499 265 V 499 266 V 499 267 V 499 267 V 499 268 V 499 268 V 498 269 V 498 270 V 498 270 V 498 271 V 498 272 V 497 272 V 497 273 V 497 273 V 496 274 V 496 274 V 496 275 V 495 275 V 495 276 V 494 277 V 494 277 V 493 278 V 493 278 V 492 279 V 492 279 V 491 280 V 491 280 V 490 280 V 489 281 V 489 281 V 488 282 V 487 282 V 486 283 V 486 283 V 485 283 V 452 312 V 452 311 V 452 310 V 452 310 V 452 309 V 452 308 V 452 308 V 452 307 V 452 307 V 453 306 V 453 305 V 453 305 V 453 304 V 454 304 V 454 303 V 454 303 V 455 302 V 455 301 V 455 301 V 456 300 V 456 300 V 457 299 V 457 299 V 458 298 V 458 298 V 459 297 V 460 297 V 460 296 V 461 296 V 461 295 V 462 295 V 463 295 V 464 294 V 464 294 V 465 293 V 466 293 V 452 265 V 452 265 V 452 266 V 452 267 V 452 267 V 452 268 V 452 269 V 453 269 V 453 270 V 453 271 V 454 271 V 454 272 V 455 273 V 455 273 V 456 274 V 456 275 V 457 275 V 457 276 V 458 277 V 459 277 V 459 278 V 460 279 V 461 279 V 462 280 V 463 281 V 464 281 V 465 282 V 466 283 V 467 283 V 468 284 V 469 285 V 470 285 V 471 286 V 473 287 V 474 288 V 475 288 V 499 312 V 499 311 V 499 310 V 499 310 V 499 309 V 498 308 V 498 308 V 498 307 V 498 306 V 497 306 V 497 305 V 497 304 V 496 304 V 496 303 V 495 302 V 495 302 V 494 301 V 493 300 V 493 300 V 492 299 V 491 298 V 490 298 V 490 297 V 489 296 V 488 296 V 487 295 V 486 294 V 485 294 V 484 293 V 483 292 V 482 292 V 480 291 V 479 290 V 478 290 V 477 289 V 475 288 V 546 312 V 546 312 V 546 313 V 546 314 V 546 314 V 546 315 V 546 316 V 546 316 V 545 317 V 545 318 V 545 318 V 545 319 V 544 319 V 544 320 V 544 320 V 544 321 V 543 322 V 543 322 V 542 323 V 542 323 V 541 324 V 541 324 V 541 325 V 540 325 V 539 326 V 539 326 V 538 327 V 538 327 V 537 328 V 536 328 V 536 329 V 535 329 V 534 329 V 534 330 V 533 330 V 532 331 V 499 359 V 499 358 V 499 358 V 499 357 V 499 356 V 499 356 V 499 355 V 499 354 V 500 354 V 500 353 V 500 353 V 500 352 V 501 351 V 501 351 V 501 350 V 502 350 V 502 349 V 502 349 V 503 348 V 503 348 V 504 347 V 504 346 V 505 346 V 505 345 V 506 345 V 506 345 V 507 344 V 507 344 V 508 343 V 509 343 V 509 342 V 510 342 V 511 341 V 512 341 V 512 340 V 513 340 V 499 312 V 499 312 V 499 313 V 499 314 V 499 314 V 499 315 V 500 316 V 500 316 V 500 317 V 500 318 V 501 319 V 501 319 V 502 320 V 502 321 V 503 321 V 503 322 V 504 323 V 504 323 V 505 324 V 506 325 V 507 325 V 507 326 V 508 327 V 509 327 V 510 328 V 511 329 V 512 329 V 513 330 V 514 331 V 515 331 V 516 332 V 517 333 V 519 333 V 520 334 V 521 335 V 523 335 V 546 359 V 546 358 V 546 358 V 546 357 V 546 356 V 546 356 V 545 355 V 545 354 V 545 354 V 545 353 V 544 352 V 544 352 V 543 351 V 543 350 V 542 350 V 542 349 V 541 348 V 541 347 V 540 347 V 539 346 V 538 345 V 538 345 V 537 344 V 536 343 V 535 343 V 534 342 V 533 341 V 532 341 V 531 340 V 530 339 V 529 339 V 528 338 V 526 337 V 525 337 V 524 336 V 523 335 V 499 359 V 499 360 V 499 360 V 499 361 V 499 362 V 499 362 V 499 363 V 498 363 V 498 364 V 498 365 V 498 365 V 498 366 V 497 366 V 497 367 V 497 368 V 496 368 V 496 369 V 496 369 V 495 370 V 495 370 V 494 371 V 494 371 V 493 372 V 493 372 V 492 373 V 492 373 V 491 374 V 491 374 V 490 375 V 489 375 V 489 376 V 488 376 V 487 377 V 486 377 V 486 377 V 485 378 V 452 406 V 452 405 V 452 405 V 452 404 V 452 404 V 452 403 V 452 402 V 452 402 V 452 401 V 453 400 V 453 400 V 453 399 V 453 399 V 454 398 V 454 397 V 454 397 V 455 396 V 455 396 V 455 395 V 456 395 V 456 394 V 457 394 V 457 393 V 458 393 V 458 392 V 459 392 V 460 391 V 460 391 V 461 390 V 461 390 V 462 389 V 463 389 V 464 389 V 464 388 V 465 388 V 466 387 V 452 359 V 452 360 V 452 360 V 452 361 V 452 362 V 452 362 V 452 363 V 453 364 V 453 364 V 453 365 V 454 366 V 454 366 V 455 367 V 455 368 V 456 368 V 456 369 V 457 370 V 457 370 V 458 371 V 459 372 V 459 372 V 460 373 V 461 374 V 462 374 V 463 375 V 464 376 V 465 376 V 466 377 V 467 378 V 468 378 V 469 379 V 470 380 V 471 381 V 473 381 V 474 382 V 475 383 V 499 406 V 499 405 V 499 405 V 499 404 V 499 403 V 498 403 V 498 402 V 498 401 V 498 401 V 497 400 V 497 399 V 497 399 V 496 398 V 496 397 V 495 397 V 495 396 V 494 395 V 493 395 V 493 394 V 492 393 V 491 393 V 490 392 V 490 391 V 489 391 V 488 390 V 487 389 V 486 389 V 485 388 V 484 387 V 483 387 V 482 386 V 480 385 V 479 385 V 478 384 V 477 383 V 475 383 V 924 265 V 924 265 V 924 266 V 923 267 V 923 267 V 923 268 V 923 268 V 923 269 V 923 270 V 923 270 V 922 271 V 922 272 V 922 272 V 922 273 V 921 273 V 921 274 V 921 274 V 920 275 V 920 275 V 919 276 V 919 277 V 918 277 V 918 278 V 917 278 V 917 279 V 916 279 V 916 280 V 915 280 V 915 280 V 914 281 V 913 281 V 912 282 V 912 282 V 911 283 V 910 283 V 909 283 V 876 312 V 876 311 V 876 310 V 877 310 V 877 309 V 877 308 V 877 308 V 877 307 V 877 307 V 877 306 V 878 305 V 878 305 V 878 304 V 878 304 V 879 303 V 879 303 V 879 302 V 880 301 V 880 301 V 881 300 V 881 300 V 882 299 V 882 299 V 883 298 V 883 298 V 884 297 V 884 297 V 885 296 V 885 296 V 886 295 V 887 295 V 888 295 V 888 294 V 889 294 V 890 293 V 891 293 V 876 265 V 876 265 V 876 266 V 877 267 V 877 267 V 877 268 V 877 269 V 877 269 V 878 270 V 878 271 V 878 271 V 879 272 V 879 273 V 880 273 V 880 274 V 881 275 V 881 275 V 882 276 V 883 277 V 883 277 V 884 278 V 885 279 V 886 279 V 887 280 V 887 281 V 888 281 V 889 282 V 890 283 V 892 283 V 893 284 V 894 285 V 895 285 V 896 286 V 897 287 V 899 288 V 900 288 V 924 312 V 924 311 V 924 310 V 923 310 V 923 309 V 923 308 V 923 308 V 923 307 V 922 306 V 922 306 V 922 305 V 921 304 V 921 304 V 920 303 V 920 302 V 919 302 V 919 301 V 918 300 V 917 300 V 917 299 V 916 298 V 915 298 V 914 297 V 913 296 V 913 296 V 912 295 V 911 294 V 910 294 V 908 293 V 907 292 V 906 292 V 905 291 V 904 290 V 903 290 V 901 289 V 900 288 V 971 453 V 971 454 V 971 455 V 971 455 V 971 456 V 970 457 V 970 457 V 970 458 V 970 458 V 970 459 V 970 460 V 969 460 V 969 461 V 969 461 V 969 462 V 968 463 V 968 463 V 967 464 V 967 464 V 967 465 V 966 465 V 966 466 V 965 466 V 965 467 V 964 467 V 964 468 V 963 468 V 962 469 V 962 469 V 961 470 V 960 470 V 960 471 V 959 471 V 958 471 V 957 472 V 957 472 V 924 501 V 924 500 V 924 499 V 924 499 V 924 498 V 924 497 V 924 497 V 924 496 V 924 495 V 925 495 V 925 494 V 925 494 V 925 493 V 926 492 V 926 492 V 926 491 V 927 491 V 927 490 V 927 490 V 928 489 V 928 489 V 929 488 V 929 488 V 930 487 V 930 487 V 931 486 V 931 486 V 932 485 V 933 485 V 933 484 V 934 484 V 935 483 V 935 483 V 936 482 V 937 482 V 938 482 V 924 453 V 924 454 V 924 455 V 924 455 V 924 456 V 924 457 V 924 457 V 925 458 V 925 459 V 925 459 V 926 460 V 926 461 V 926 461 V 927 462 V 927 463 V 928 463 V 929 464 V 929 465 V 930 465 V 931 466 V 931 467 V 932 467 V 933 468 V 934 469 V 935 469 V 936 470 V 937 471 V 938 472 V 939 472 V 940 473 V 941 474 V 942 474 V 943 475 V 945 476 V 946 476 V 947 477 V 971 501 V 971 500 V 971 499 V 971 498 V 970 498 V 970 497 V 970 496 V 970 496 V 970 495 V 969 494 V 969 494 V 968 493 V 968 492 V 968 492 V 967 491 V 966 490 V 966 490 V 965 489 V 965 488 V 964 488 V 963 487 V 962 486 V 961 486 V 961 485 V 960 484 V 959 484 V 958 483 V 957 482 V 956 482 V 955 481 V 953 480 V 952 480 V 951 479 V 950 478 V 949 478 V 947 477 V 1537 406 V 1537 407 V 1537 407 V 1537 408 V 1537 409 V 1537 409 V 1537 410 V 1536 411 V 1536 411 V 1536 412 V 1536 412 V 1536 413 V 1535 414 V 1535 414 V 1535 415 V 1534 415 V 1534 416 V 1534 416 V 1533 417 V 1533 418 V 1532 418 V 1532 419 V 1531 419 V 1531 420 V 1530 420 V 1530 421 V 1529 421 V 1529 422 V 1528 422 V 1527 422 V 1527 423 V 1526 423 V 1525 424 V 1524 424 V 1524 425 V 1523 425 V 1490 453 V 1490 453 V 1490 452 V 1490 451 V 1490 451 V 1490 450 V 1490 449 V 1490 449 V 1491 448 V 1491 448 V 1491 447 V 1491 446 V 1491 446 V 1492 445 V 1492 445 V 1492 444 V 1493 444 V 1493 443 V 1494 442 V 1494 442 V 1494 441 V 1495 441 V 1495 440 V 1496 440 V 1496 439 V 1497 439 V 1498 438 V 1498 438 V 1499 437 V 1500 437 V 1500 437 V 1501 436 V 1502 436 V 1502 435 V 1503 435 V 1504 434 V 1490 406 V 1490 407 V 1490 407 V 1490 408 V 1490 409 V 1490 410 V 1490 410 V 1491 411 V 1491 412 V 1491 412 V 1492 413 V 1492 414 V 1493 414 V 1493 415 V 1494 416 V 1494 416 V 1495 417 V 1495 418 V 1496 418 V 1497 419 V 1498 420 V 1498 420 V 1499 421 V 1500 422 V 1501 422 V 1502 423 V 1503 424 V 1504 424 V 1505 425 V 1506 426 V 1507 426 V 1508 427 V 1510 428 V 1511 428 V 1512 429 V 1513 430 V 1537 453 V 1537 453 V 1537 452 V 1537 451 V 1537 451 V 1537 450 V 1536 449 V 1536 449 V 1536 448 V 1535 447 V 1535 447 V 1535 446 V 1534 445 V 1534 445 V 1533 444 V 1533 443 V 1532 443 V 1531 442 V 1531 441 V 1530 441 V 1529 440 V 1528 439 V 1528 438 V 1527 438 V 1526 437 V 1525 436 V 1524 436 V 1523 435 V 1522 434 V 1521 434 V 1520 433 V 1518 432 V 1517 432 V 1516 431 V 1515 430 V 1513 430 V 497 459 2 7 v 497 478 a Fe(\006)p 544 459 V 14 w(\005)p 516 478 14 2 v 521 483 2 7 v 521 501 a(\006)p 568 483 V 14 w(\005)p 539 501 14 2 v 875 412 2 7 v 875 431 a(\006)p 922 412 V 14 w(\005)p 893 431 14 2 v 969 507 2 7 v 969 525 a(\006)p 1016 507 V 14 w(\005)p 987 525 14 2 v 1535 459 2 7 v 1535 478 a(\006)p 1583 459 V 15 w(\005)p 1554 478 14 2 v 570 477 2 2 v 570 476 V 570 475 V 570 475 V 570 474 V 570 473 V 570 472 V 570 471 V 570 471 V 570 470 V 570 469 V 571 468 V 571 468 V 571 467 V 571 466 V 571 466 V 572 465 V 572 464 V 572 464 V 572 463 V 573 462 V 573 462 V 573 461 V 574 460 V 574 460 V 575 459 V 575 458 V 575 458 V 576 457 V 576 457 V 577 456 V 577 456 V 578 455 V 578 454 V 579 454 V 579 453 V 579 453 V 580 453 V 581 452 V 581 452 V 582 451 V 583 451 V 584 450 V 584 449 V 585 449 V 585 448 V 586 448 V 587 447 V 587 446 V 588 446 V 588 445 V 589 444 V 589 444 V 590 443 V 590 442 V 590 442 V 591 441 V 591 440 V 591 440 V 592 439 V 592 438 V 592 437 V 592 437 V 593 436 V 593 435 V 593 434 V 593 434 V 593 433 V 593 432 V 593 431 V 593 431 V 593 430 V 924 453 V 924 453 V 924 453 V 924 453 V 923 452 V 923 452 V 923 452 V 923 451 V 923 451 V 923 451 V 923 451 V 923 450 V 922 450 V 922 450 V 922 450 V 922 449 V 922 449 V 921 449 V 921 448 V 921 448 V 921 448 V 920 448 V 920 447 V 920 447 V 919 447 V 919 447 V 918 446 V 918 446 V 918 446 V 917 446 V 917 445 V 916 445 V 916 445 V 915 444 V 915 444 V 914 444 V 914 444 V 913 443 V 913 443 V 912 442 V 911 442 V 910 441 V 910 441 V 909 440 V 908 440 V 908 439 V 907 439 V 907 438 V 906 438 V 906 438 V 905 437 V 905 437 V 904 436 V 904 436 V 903 435 V 903 435 V 903 435 V 902 434 V 902 434 V 902 434 V 901 433 V 901 433 V 901 432 V 901 432 V 901 432 V 900 431 V 900 431 V 900 431 V 900 431 V 900 430 V 900 430 V 900 430 V 499 547 a(r)p 452 501 V 452 502 V 452 503 V 452 505 V 452 506 V 453 507 V 453 509 V 454 510 V 454 511 V 455 513 V 456 514 V 456 515 V 457 517 V 458 518 V 459 519 V 460 521 V 462 522 V 463 523 V 464 525 V 466 526 V 467 527 V 469 529 V 470 530 V 472 532 V 474 533 V 476 534 V 478 536 V 480 537 V 482 538 V 484 540 V 486 541 V 489 542 V 491 544 V 494 545 V 496 546 V 499 548 V 546 501 V 546 502 V 546 503 V 546 505 V 546 506 V 545 507 V 545 509 V 544 510 V 544 511 V 543 513 V 542 514 V 541 515 V 541 517 V 540 518 V 539 519 V 537 521 V 536 522 V 535 523 V 534 525 V 532 526 V 531 527 V 529 529 V 527 530 V 526 532 V 524 533 V 522 534 V 520 536 V 518 537 V 516 538 V 514 540 V 511 541 V 509 542 V 507 544 V 504 545 V 502 546 V 499 548 V 460 w(r)p 924 501 V 924 502 V 924 503 V 924 505 V 924 506 V 925 507 V 925 509 V 925 510 V 926 511 V 927 513 V 927 514 V 928 515 V 929 517 V 930 518 V 931 519 V 932 521 V 933 522 V 935 523 V 936 525 V 937 526 V 939 527 V 941 529 V 942 530 V 944 532 V 946 533 V 948 534 V 950 536 V 952 537 V 954 538 V 956 540 V 958 541 V 961 542 V 963 544 V 966 545 V 968 546 V 971 548 V 994 524 V 994 525 V 994 526 V 994 526 V 994 527 V 994 528 V 994 529 V 993 530 V 993 530 V 993 531 V 992 532 V 992 533 V 992 533 V 991 534 V 991 535 V 990 535 V 989 536 V 989 537 V 988 537 V 987 538 V 987 539 V 986 540 V 985 540 V 984 541 V 983 541 V 982 542 V 981 543 V 980 543 V 979 544 V 978 544 V 977 545 V 976 546 V 975 546 V 973 547 V 972 547 V 971 548 V 1513 523 a(r)p 1490 501 V 1490 501 V 1490 502 V 1490 503 V 1490 504 V 1490 504 V 1490 505 V 1491 506 V 1491 507 V 1491 507 V 1492 508 V 1492 509 V 1493 510 V 1493 510 V 1494 511 V 1494 512 V 1495 512 V 1495 513 V 1496 514 V 1497 514 V 1498 515 V 1498 516 V 1499 516 V 1500 517 V 1501 518 V 1502 518 V 1503 519 V 1504 520 V 1505 520 V 1506 521 V 1507 521 V 1508 522 V 1510 522 V 1511 523 V 1512 524 V 1513 524 V 1561 477 V 1561 478 V 1560 480 V 1560 481 V 1560 482 V 1560 484 V 1559 485 V 1559 486 V 1558 488 V 1557 489 V 1557 490 V 1556 492 V 1555 493 V 1554 494 V 1553 496 V 1552 497 V 1551 498 V 1549 500 V 1548 501 V 1547 503 V 1545 504 V 1544 505 V 1542 507 V 1540 508 V 1538 509 V 1537 511 V 1535 512 V 1533 513 V 1530 515 V 1528 516 V 1526 517 V 1524 519 V 1521 520 V 1519 521 V 1516 523 V 1513 524 V 187 377 a Fz(=)235 374 y(\()p Ft(\000)p Fz(1\))336 356 y Fx(n)p Fq(+1)403 336 y Fy(\031)431 343 y Fx(n)481 448 y Fy(A)439 226 y Ff(g)e(g)500 208 y Fx(n)526 235 y Fy(V)20 b(V)617 377 y Fz(=)659 374 y(\()p Ft(\000)p Fz(1\))760 356 y Fx(n)p Fq(+1)827 336 y Fy(\031)855 343 y Fx(n)858 401 y Fy(A)864 226 y Ff(g)10 b(g)924 208 y Fx(n)951 235 y Fy(V)19 b(V)1046 377 y Fz(=)1098 374 y(\()p Ft(\000)p Fz(1\))1199 356 y Fx(n)p Fq(+1)1269 333 y Ft(r)1311 315 y Fx(n)p Fq(+1)1379 333 y Fy(\031)1407 340 y Fx(n)p Fq(+1)1472 401 y Fy(A)1434 226 y Ff(g)1459 208 y Fx(n)p Fq(+1)1517 235 y Fy(V)h(V)0 659 y Fz(In)h(the)g(\014rst)g(and)h(the)f(last)g(term)f(w)o(e)g (indicated)h(the)f(m)o(ultiplication)e Ft(r)1409 641 y Fx(n)1455 659 y Fz(:)j Ff(g)1515 641 y Fx(n)1561 659 y Ft(\000)-30 b(!)22 b Fy(A)e Fz(resp.)0 717 y Ft(r)42 699 y Fx(n)p Fq(+1)124 717 y Fz(:)13 b Ff(g)176 699 y Fx(n)p Fq(+1)259 717 y Ft(\000)-30 b(!)13 b Fy(A)p Fz(.)21 b(F)l(urthermore)14 b(w)o(e)i(indicated)g(the)g(use)g(of)g Fy(\031)1220 724 y Fx(n)1260 717 y Fz(where)g(appropriate.)50 784 y(No)o(w)f(let)f Fy(\020)20 b Fz(b)q(e)15 b(a)h(primitiv)o(e)c Fy(n)p Fz(-th)j(ro)q(ot)i(of)e(unit)o(y)g(and)g Fy(z)h Ft(2)e Ff(g)1178 766 y Fx(n)1202 784 y Fz(\()p Fy(\020)t Fz(\).)21 b(Then)15 b Fy(\020)1456 749 y Fw(n)p Fl(\()p Fw(n)p Fm(\000)p Fl(1\))p 1456 758 102 2 v 1499 779 a(2)1579 784 y Fz(=)e(\()p Ft(\000)p Fz(1\))1731 766 y Fx(n)p Fs(\000)p Fq(1)0 855 y Fz(and)j Fy(\031)122 862 y Fx(n)146 855 y Fz(\()p Fy(z)r Fz(\))d(=)h Fy(\020)304 820 y Fw(n)p Fl(\()p Fw(n)p Fm(\000)p Fl(1\))p 304 829 V 347 849 a(2)413 855 y Fy(\032)438 862 y Fx(n)461 855 y Fz(\()p Fy(z)r Fz(\))i(b)o(y)f(\(7\))i(and)f(the)g(de\014nition)f(of)h Fy(\031)1163 862 y Fx(n)1186 855 y Fz(,)g(where)f Fy(\032)1381 862 y Fx(n)1421 855 y Fz(is)h(the)f(image)g(of)h Fy(\031)1777 862 y Fx(n)0 913 y Fz(under)g(the)g(canonical)g(map)g Fy(B)582 920 y Fx(n)619 913 y Ft(\000)-30 b(!)13 b Fy(S)721 920 y Fx(n)745 913 y Fz(.)21 b(So)c(w)o(e)f(get)190 1002 y Fy(\026)p Fz(\()p Fy(#)11 b Ft(\012)g Fz(1\)\([)p Fy(z)r Fz(])f Ft(\012)h Fy(v)i Ft(\012)e Fy(w)q Fz(\))j(=)371 1060 y(=)423 1023 y Fo(P)476 1074 y Fx(\033)508 1060 y Fy(\026)p Fz(\()p Fy(#)d Ft(\012)f Fz(1\)\()p Ft(r)749 1042 y Fx(n)773 1060 y Fy(\033)r Fz(\()p Fy(z)r Fz(\))g Ft(\012)h Fy(v)h Ft(\012)f Fy(w)q Fz(\))371 1118 y(=)423 1081 y Fo(P)476 1133 y Fx(\033)508 1118 y Fy(\026)p Fz(\()p Fy(#)g Ft(\012)f Fz(1\)\()p Ft(r)749 1100 y Fx(n)784 1118 y Ft(\012)h Fz(1)g Ft(\012)g Fz(1\)\()p Fy(\033)r Fz(\()p Fy(z)r Fz(\))g Ft(\012)f Fy(v)j Ft(\012)e Fy(w)q Fz(\))371 1176 y(=)j(\()p Ft(\000)p Fz(1\))524 1158 y Fx(n)556 1139 y Fo(P)609 1191 y Fx(\033)640 1176 y Fy(\026)p Fz(\(1)e Ft(\012)f Fy(#)p Fz(\)\()p Fy(\034)16 b Ft(\012)11 b Fz(1\)\()p Ft(r)1032 1158 y Fx(n)1056 1176 y Fy(\031)1084 1183 y Fx(n)1118 1176 y Ft(\012)g Fz(1)g Ft(\012)g Fz(1\)\()p Fy(\033)r Fz(\()p Fy(z)r Fz(\))g Ft(\012)f Fy(v)j Ft(\012)e Fy(w)q Fz(\))371 1234 y(=)j(\()p Ft(\000)p Fz(1\))532 1197 y Fo(P)585 1249 y Fx(\033)617 1234 y Fy(\026)p Fz(\(1)e Ft(\012)e Fy(#)p Fz(\)\()p Fy(\034)17 b Ft(\012)11 b Fz(1\)\()p Ft(r)1009 1216 y Fx(n)1043 1234 y Ft(\012)g Fz(1)g Ft(\012)g Fz(1\)\()p Fy(\032)1265 1241 y Fx(n)1289 1234 y Fy(\033)r Fz(\()p Fy(z)r Fz(\))g Ft(\012)f Fy(v)j Ft(\012)e Fy(w)q Fz(\))371 1292 y(=)j(\()p Ft(\000)p Fz(1\))p Fy(\026)p Fz(\(1)e Ft(\012)f Fy(#)p Fz(\)\()p Fy(\034)16 b Ft(\012)11 b Fz(1\)\([)p Fy(z)r Fz(])g Ft(\012)f Fy(v)j Ft(\012)e Fy(w)q Fz(\))p Fy(;)0 1386 y Fz(hence)k([)p Fy(z)r Fz(])e Ft(2)h Ff(g)p Fz(.)22 b(Th)o(us)16 b Ff(g)h Fz(is)f(a)g(Lie)g(subalgebra)h(of)g Fr(end)r Fz(\()p Fy(V)11 b Fz(\).)647 b Fk(\003)379 1524 y Fz(7.)24 b FA(Lie)19 b(str)o(uctures)f(on)g Fy(C)953 1531 y Fx(p)971 1522 y Fw(n)994 1524 y FA(-graded)h(modules)50 1611 y Fz(In)k(this)h(section)f(w)o(e)g(assume)g(that)h Fy(G)j Fz(=)g Fy(C)924 1619 y Fx(p)942 1610 y Fw(t)984 1611 y Fz(=)f Fj(Z)-10 b Fy(=)p Fz(\()p Fy(p)1152 1593 y Fx(t)1164 1611 y Fz(\))24 b(is)g(the)f(cyclic)f(group)i(with)g Fy(p)1785 1593 y Fx(t)0 1670 y Fz(elemen)o(ts)11 b(where)i Fy(p)h Ft(6)p Fz(=)g(2)f(is)g(prime)f(and)i(that)f(the)h(\014eld)e Fy(k)k Fz(has)e(c)o(haracteristic)e Ft(6)p Fz(=)h(2)h(and)g(con)o (tains)0 1728 y(a)24 b Fy(p)72 1710 y Fx(t)87 1728 y Fz(-th)h(primitiv)n(e)c(ro)q(ot)k(of)f(unit)o(y)f Fy(\030)r Fz(.)44 b(W)l(e)24 b(w)o(an)o(t)g(to)g(get)f(information)g(on)i(the)e (non)o(trivial)0 1786 y(symmetri)o(zations)14 b(of)j Fy(G)p Fz(-como)q(dules.)50 1844 y(A)k(bic)o(haracter)g Fy(\037)h Fz(:)h Fy(G)15 b Ft(\012)549 1851 y Fc(Z)588 1844 y Fy(G)24 b Ft(\000)-31 b(!)23 b Fy(k)758 1826 y Fs(\002)809 1844 y 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y(unchen,)i(Germany)50 1882 y Fv(E-mail)d(addr)n (ess)s FC(:)19 b Fa(pareigis@rz.math)o(emat)o(ik.un)o(i-mue)o(nchen)o (.de)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF