Acta mathematica scientia, Series B >
MORITA CONTEXT OF WEAK HOPF ALGEBRAS
Received date: 2008-09-29
Revised date: 2010-01-30
Online published: 2011-05-20
Supported by
Supported by the NSF of China (10971049; 10971052) and the NSF of Hebei Province (A2008000135; A2009000253).
Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra AH. 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 <AH, A#H, A,A, τ, μ connecting the smash product A#H and the invariant subalgebra AH, which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.
Key words： weak Hopf algebras; A-rings; morita context; Frobenius extension
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 . DOI: 10.1016/S0252-9602(11)60304-4
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