Polynomial vector fields on \(K^ n\) as a \(GL_ n(K)\)-module (Q1058596)
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scientific article; zbMATH DE number 3901027
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polynomial vector fields on \(K^ n\) as a \(GL_ n(K)\)-module |
scientific article; zbMATH DE number 3901027 |
Statements
Polynomial vector fields on \(K^ n\) as a \(GL_ n(K)\)-module (English)
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1985
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Let K be a commutative \({\mathbb{Q}}\)-algebra, \(K^{[n]}\) the polynomial ring over K in n variables (n\(\geq 2)\) and L the Lie algebra of all K- derivations from \(K^{[n]}\) to \(K^{[n]}\). The group \(G:=GL(n,K)\) acts by linear change of variables on \(K^{[n]}\) and then by conjugation on L. The author studies the G-invariant additive subgroups of L and classifies them by certain pairs of sequences of ideals in K.
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polynomial vector fields
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Lie algebra of derivations
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conjugation
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G- invariant additive subgroups
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sequences of ideals
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