MORITA CONTEXT OF WEAK HOPF ALGEBRAS

doi:10.1016/S0252-9602(11)60304-4

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (3): 1133-1141.doi: 10.1016/S0252-9602(11)60304-4

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MORITA CONTEXT OF WEAK HOPF ALGEBRAS

HOU Bo, ZHANG Zi-Long, CAI Bing-Lian, LI Yan

College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China|Department of Mathematics and Information Science, Tangshan Teacher's College, Tangshan 063000, China

Received:2008-09-29 Revised:2010-01-30 Online:2011-05-20 Published:2011-05-20
Supported by:
Supported by the NSF of China (10971049; 10971052) and the NSF of Hebei Province (A2008000135; A2009000253).

Abstract

Abstract:

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.

Key words: weak Hopf algebras, A-rings, morita context, Frobenius extension

CLC Number:

16W30

HOU Bo, ZHANG Zi-Long, CAI Bing-Lian, LI Yan. MORITA CONTEXT OF WEAK HOPF ALGEBRAS[J].Acta mathematica scientia,Series B, 2011, 31(3): 1133-1141.

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MORITA CONTEXT OF WEAK HOPF ALGEBRAS

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