Hopf群余代数的结构定理.pdf

ISSN1003—7985 JournalofSoutheast Mar．2013 University(EnglishEdition)V01．29，No．1，PP．103—105 Structuretheoremfor Hopfgroup-coalgebra DongLihon91-2WangShengxian91WangShuanhon91 1 (1 ofMathematics，Southeast21189，China) Department University，Nanjing of andInformation Normal (2 Mathematics Science，Henan 453007，China) College University，Xinxiang Abstract：Let7／bea witha unitl：Hisa 77-一 SUITSabout introducedTuraev【3】． group Hopf by Hopf仃．coalgebras andAisa 7r．皿comodule re— coalgebra fight algebra．First．the this kbeafield．Thereaderis Throughoutpaper，let notionofa two—sided is relative(A，日)．Hopf仃一comodule ferredtoSweedler‘81about Hopfalgebras． itisobtainedtllat Hand introduced；then Hom：(MⅣ)0 as 1．1 Semi-Hopf∞-coalgebra 7／-·H-comodules， HOM^(MⅣ)areisomorphicfightHopf where denotesthe of A—module right Hom：(M,M space right RecallfromTuraev㈣thata isa of 7r．coalgebrafamily H-comoduleand the morphismsHOM。(M加denotesrational