MORITA CONTEXT OF WEAK HOPF ALGEBRAS  

作　　者：候波 张子龙 蔡炳苓 李燕 

机构地区：[1]College of Mathematics and Information Science Hebei Normal University [2]Department of Mathematics and Information Science Tangshan Teacher's College

出　　处：《Acta Mathematica Scientia》2011年第3期1133-1141,共9页数学物理学报（B辑英文版）

基　　金：Supported by the NSF of China(10971049;10971052);the NSF of Hebei Province(A2008000135;A2009000253)

摘　　要：Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A^H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context 〈A^H,A#H,A,A,τ,μ〉 connecting the smash product A#H and the invariant subalgebra A^H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A^H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context 〈A^H,A#H,A,A,τ,μ〉 connecting the smash product A#H and the invariant subalgebra A^H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.

关 键 词：weak Hopf algebras A-rings morita context Frobenius extension 

分 类 号：O153[理学—数学]