Cosemisimple Coextensions and Homological Dimension of Smash Coproducts  

作　　者：Jia Gui ZHU 

机构地区：[1]Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China [2]Department of Mathematics, West Anhui University, Lu'an 237012, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2005年第3期563-568,共6页数学学报（英文版）

基　　金：Supported by the Foundation of Key Research Program (No. 02021029);the NSF (No. 2004kj352) of Anhui Province, China

摘　　要：Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.

关 键 词：COALGEBRA Homological dimension Smash coproduct Hopf algebra 

分 类 号：O15[理学—数学]