Notes on the Drinfeld double of finite-dimensional group algebras. (Q2909077)
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scientific article; zbMATH DE number 6073849
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Notes on the Drinfeld double of finite-dimensional group algebras. |
scientific article; zbMATH DE number 6073849 |
Statements
29 August 2012
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Hopf algebras
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group algebras
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tensor products of representations
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Drinfeld doubles
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Chevalley property
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Notes on the Drinfeld double of finite-dimensional group algebras. (English)
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Suppose that \(k\) is an algebraically closed field of positive characteristic \(p\). The main result of the paper is a characterization of those finite groups \(G\) for which the Drinfeld double \(D(kG)\) of the group algebra \(kG\) has the Chevalley property. It means that the tensor product of any two irreducible representations of \(G\) is semisimple. There is found the largest Hopf ideal in the Jacobson radical of \(D(kG)\)
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