On linear subspaces of nilpotent elements in a Lie algebra (Q1307569)
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scientific article; zbMATH DE number 1355349
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On linear subspaces of nilpotent elements in a Lie algebra |
scientific article; zbMATH DE number 1355349 |
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On linear subspaces of nilpotent elements in a Lie algebra (English)
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6 December 1999
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Let \(L\) be a complex semisimple Lie algebra. The authors show that if \(W\) is a linear subspace of ad-nilpotent elements, then \(\dim W\leq \frac 12(\dim L-\operatorname {rank }L)\). They also prove that the maximal dimension of a linear space of symmetric nilpotent \(n\times n\) complex matrices is \(\frac 14 n^2\).
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nilpotent matrices
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spaces of matrices
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semisimple Lie algebra
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