; TeX output 2002.04.24:13497 VN cmbx12MathematischesInstitutSS2002derUniversitXatM`unchenSet2Prof.Dr.B.Pareigis;KrNff cmbx12Problemffsetfor&QuantumffGroupsandNoncommutativeGeometry,XQ cmr12(5)%Letz%!", cmsy10X;denotetheplanecurvreg cmmi12yË=URx2|{Ycmr82._ThenXisisomorphictotheaneline.ʍ(6)%〟2 K cmsy8-ֹLet:R( msbm10KbSeanalgebraicallyclosed eld.Letpbeanirreduciblesquarepolyno-%mialMinK[x;yn9].LetZA͹bSetheconicsectionde nedbrypwiththeanealgebra%K[x;yn9]=(p).ShorwϥthatZñisnaturallyisomorphiceithertoXxortoUfrom%problems(3)resp.8(5).(7)%LetX{bSeananescrhemewithanealgebraeAUR=K[x1;:::ʜ;x2cmmi8nP]=(p1;:::ʜ;pmĹ):%〹De ne \coSordinatefunctions"qi,:URXӹ(B)n!1Bywhicrh describethecoordinates%ofB-pSoinrtsandidentifythesecoSordinatefunctionswithelementsofA.(8)%Let^/S3 3bSethesymmetricgroupandA:=K[S3]^/bethegroupalgebraonS3.%DescribSeithepoinrtsofXӹ(B)UR=K-A+@ cmti12lg f(A;B)iasasubspaceofA22(B).Whatis%thecommrutativepartXc.y(B)ofX{andwhatistheanealgebraofXc?=}Duedate:8TVuesdary,30.04.2002,16:15inLectureHallE41*;7 +@ cmti12( msbm10 K cmsy8!", cmsy102cmmi8g cmmi12|{Ycmr8Nff cmbx12N cmbx12XQ cmr12