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...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.展开更多
R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the con...R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the concept of Hopf comodule coalgebras which is a dual notation of Hopf module algebra, and discussed their properties. However, the duality theorem of Hopf comodule coalgebras has not been proved yet. In this note we shall deal with this situation by defining the展开更多
基金Supported by National Natural Science Foundation of China(10871170)Educational Minister Science Technology Key Foundation of China(10871170)College Special Research Doctoral Disciplines Point Fund of China(20100097110040)
基金the Educational Ministry Science Technique Research Key Foundation of China(108154)the College Special Research Doctoral Disciplines point Fund(2010097110040)+2 种基金the National Natural Science Foundation of China(10871170)the National Natural Science Foundation of Guangxi(2011GXNSFA018144)the Fundamental Research Funds for the Central Universities(KYZ201125)
基金Supported by the Foundation of Key Research Program (No. 02021029)the NSF (No. 2004kj352) of Anhui Province, China
文摘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.
文摘R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the concept of Hopf comodule coalgebras which is a dual notation of Hopf module algebra, and discussed their properties. However, the duality theorem of Hopf comodule coalgebras has not been proved yet. In this note we shall deal with this situation by defining the
