; TeX output 2002.03.07:10567 VN cmbx12MathematischesInstitutSS2002derUniversitXatM`unchenSet1Prof.Dr.B.Pareigis;KrNff cmbx12Problemffsetfor&QuantumffGroupsandNoncommutativeGeometry=}XQ cmr12(1)%Determinetheanealgebraofthefunctor\unitsphere"g cmmi12Sן22cmmi8n K cmsy8|{Ycmr81"Kin( msbm10A2nP.ʍ(2)%Determinetheanealgebraofthefunctor\torus"!", cmsy10Tܹand ndan\emrbSedding"%ofTuinrtoA23.(3)%LetgU&xdenotetheplanecurvrexyչ=g1.YThenUisnotisomorphictotheane%line. (Hinrt:An0isomorphismK[x;x21 \|]̋!K[yn9]sendsxtoapSolynomialp(y)%whicrhHmustbSeinvertible.bConsiderthehighestcoSecientofp(yn9)andshow%thatp(yn9)UR2K.8ButthatmeansthatthemapcannotbSebijectivre.)%Uisalsocalledthe+@ cmti12unit35functor.8Canyrouexplain,why?(4)%LetbKP=CbSethe eldofcomplexnrumbSers. Showthattheunitfunctor%U8:K-c Algm! SetYinS Problem(3)isnaturallyisomorphictotheunitcircle%Sן21r۹.(Hinrt:There isanalgebraisomorphismbSetweentherepresentingalgebras%K[e;e21 \|]andK[c;s]=(c22j+s221).)=}Duedate:8TVuesdary,23.04.2002,16:15inLectureHallE41*;7 +@ cmti12( msbm10 K cmsy8!", cmsy102cmmi8g cmmi12|{Ycmr8Nff cmbx12N cmbx12XQ cmr12