Actions of Semisimple Weak Hopf Algebras |
Received:June 06, 2006 Revised:January 16, 2007 |
Key Words:
Weak Hopf algebras Gorenstein algebras Injective dimension.
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Fund Project:the National Natural Science Foundation of China (No. 10301033; 10271113). |
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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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