A note on symmetrizing forms for fully group-graded algebras (Q5936199)
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scientific article; zbMATH DE number 1616327
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on symmetrizing forms for fully group-graded algebras |
scientific article; zbMATH DE number 1616327 |
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A note on symmetrizing forms for fully group-graded algebras (English)
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4 April 2002
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Let \(G\) be a finite group, \(O\) a commutative ring, and \(R\) a fully \(G\)-graded \(O\)-algebra. The main result of the paper states that if \(R_1\) is a direct sum of full matrix rings over \(O\), then there is a \(G\)-invariant symmetrizing form for \(R_1\), and consequently, \(R\) is a symmetric \(O\)-algebra.
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finite groups
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group graded algebras
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symmetric algebras
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matrix algebras
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