; TeX output 2002.05.23:12407 VN cmbx12MathematischesInstitutSS2002derUniversitXatM`unchenSet6Prof.Dr.B.Pareigis;KrNff cmbx12Problemffsetfor&QuantumffGroupsandNoncommutativeGeometry, XQ cmr12(21)%LetxXg cmmi12HebSeaHopfalgebra.ThenS+/isananrtihomomorphismofalgebrasand%coalgebrasCBi.e.BS\inrvertstheorderofthemultiplicationandthecomultipli-%cation".ʍ (22)%LetuHc'andKRobSeHopfalgebrasandletf0:B1H/!", cmsy10I!EKbSeahomomorphismof%bialgebras.8ThenfGS2cmmi8H n=URSK;f,i.e.8f2iscompatiblewiththeanrtipSode. (23)%Let^0( msbm10KbSea eld.yShorwthatanelementx2KG^0satis es(x)=xQ x^0and%"(x)UR=1ifandonlyifxUR=gË2G. (24))((a)=ѬShorw) thatthegrouplikeelementsofaHopfalgebraformagroupunder=ѬmrultiplicationoftheHopfalgebra.)' (b)=ѬShorwthatthesetofprimitiveelementsPƹ(HV)UR=fx2Hj(x)=xn 1+=Ѭ1 xg꨹ofaHopfalgebraHisaLiesubalgebraofHV2L5..=}Duedate:8TVuesdary,04.06.2002,16:15inLectureHallE41*;7 ( msbm10!", cmsy102cmmi8g cmmi12Nff cmbx12N cmbx12XQ cmr12j