L'ensemble des algèbres de Lie algébriques n'est pas Zariski-dense dans la variété des algèbres de Lie de dimension m\(\geq 9\). (The set of algebraic Lie algebras is not Zariski dense in the variety of Lie algebras of dimension m\(\geq 9)\) (Q1104399)
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scientific article; zbMATH DE number 4055846
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | L'ensemble des algèbres de Lie algébriques n'est pas Zariski-dense dans la variété des algèbres de Lie de dimension m\(\geq 9\). (The set of algebraic Lie algebras is not Zariski dense in the variety of Lie algebras of dimension m\(\geq 9)\) |
scientific article; zbMATH DE number 4055846 |
Statements
L'ensemble des algèbres de Lie algébriques n'est pas Zariski-dense dans la variété des algèbres de Lie de dimension m\(\geq 9\). (The set of algebraic Lie algebras is not Zariski dense in the variety of Lie algebras of dimension m\(\geq 9)\) (English)
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1989
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The set of algebraic Lie algebras is dense in the variety \(L_ m\) of Lie algebras of dimension \(m\leq 7\). This fact allowed \textit{Y. Diakité} and the author [J. Algebra 91, 53-63 (1984; Zbl 0546.17006)] to study the varieties \(L_ m\) for \(m\leq 7\). In this article we build for \(m\geq 9\) a family of non empty open sets consisting of non decomposable laws (thus non algebraic).
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algebraic Lie algebras
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varieties of Lie algebras
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0.8404878377914429
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0.7798147797584534
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