The algebra of the subspace semigroup of \(M_2(\mathbb{F}_q)\) (Q2773363)
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scientific article; zbMATH DE number 1709953
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The algebra of the subspace semigroup of \(M_2(\mathbb{F}_q)\) |
scientific article; zbMATH DE number 1709953 |
Statements
21 February 2002
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subspace semigroups
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complex semigroup algebras
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matrices over finite fields
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The algebra of the subspace semigroup of \(M_2(\mathbb{F}_q)\) (English)
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Let \(M_n(K)\) be the algebra of all \(n\times n\) matrices over a field \(K\) and let \(S(M_n(K))\) be the semigroup formed by all subspaces of \(M_n(K)\) with the operation \(V*W=\text{lin}_K(VW)\). A description of all regular \(\mathcal J\)-classes of \(M_2(K)\) over a finite field \(K\) is given. As a consequence, the structure of the complex semigroup algebra \(\mathbb{C}(S(M_2(K)))\) is obtained.
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