Subalgebras of nilpotent matrices (Q2739146)
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scientific article; zbMATH DE number 1643519
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Subalgebras of nilpotent matrices |
scientific article; zbMATH DE number 1643519 |
Statements
1 December 2002
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loop
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nilpotent subalgebra
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total matrix algebra
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Subalgebras of nilpotent matrices (English)
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The authors consider the subalgebras of the total matrix algebra \(M(n,K)\) \((K\) a field) generated by a set of matrix units \(E_{ij}\). Their main result is that the subalgebra is nilpotent if and only if no ``loop'' \((i_1,i_2)\), \((i_2,i_3), \dots,(i_m,i_1)\), \(m\geq 1\) can be formed with the corresponding index pairs \((i,j)\).
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