Actions of Semisimple Weak Hopf Algebras
Received:June 06, 2006  Revised:January 16, 2007
Key Words: Weak Hopf algebras   Gorenstein algebras   Injective dimension.  
Fund Project:the National Natural Science Foundation of China (No. 10301033; 10271113).
Author NameAffiliation
GAO Nan Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China 
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Abstract:
      Let $H$ be a semisimple weak Hopf algebra, $A$ a left $H$-module algebra. We prove that the injective dimension of the regular $A$-module is equal to the one of $A$ as the module over the smash product $A\#H$, and equal to the one of the regular $A\#H$-module. Also, we give a necessary and sufficient condition for $A$ being a Gorenstein algebra, in terms of the fixed subalgebra of $A$ under the action of $H$ on $A$.
Citation:
DOI:10.3770/j.issn:1000-341X.2008.01.004
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