; TeX output 2002.02.27:15127 VN cmbx12MathematischesInstitutSS2002derUniversitXatM`unchen".Set3Prof.Dr.B.Pareigis;KNff cmbx12Problemffsetfor80QuantumffGroupsandNoncommutativeGeometry {cXQ cmr12(9)%Considerthefollorwingsubset( msbm10Hofthesetofcomplex2!", cmsy102-matrices:Q}pHUR:=q"u cmex10 USqʍ*g cmmi12x*y8rly//@ox?V3qK2M)ppmsbm8CG(22)jx;yË2URCq>%〹WVecallHthesetof+@ cmti12Hamiltonian35quaternions.8For>hUR=qʍ*x!y8qly&&@nx6V2q%〹wrede ne:썍W) * h#ù:=URqʍMUx*y*ˎy*x6V2qs%〹Shorw:)((a)=ѬhW9*h ܹ=UR(jxj2|{Ycmr82j+jyn9j22)E(Etheunitmatrix),)' (b)=ѬH꨹isarealsubalgebraofthecomplexalgebraof22-matrices.*uD(c)=ѬHcisadivisionalgebra,Ei.e.eacrhelementdi erentfromzerohasaninverseunder=Ѭthemrultiplication.)' (d)=ѬLetQZ@ ğ>RHD6Xӹ(B)[Ǡ*Ffe؎Ǡ?`f1l%〹commrutes. (12)%DetermineXexplicitlythedualcoalgebraA2 \ofthealgebraA:=Khxi=(x22).(Hinrt:%FindabasisforA.)cDuedate:8TVuesdary,07.05.2002,16:15inLectureHallE41 J;7 G ,o cmr9+@ cmti12)ppmsbm8( msbm10"u cmex10 K cmsy8!", cmsy102cmmi8g cmmi12|{Ycmr8Nff cmbx12N cmbx12XQ cmr12O line10X