\(n\)-Poisson and \(n\)-Sklyanin brackets (Q1608124)
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scientific article; zbMATH DE number 1777798
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(n\)-Poisson and \(n\)-Sklyanin brackets |
scientific article; zbMATH DE number 1777798 |
Statements
\(n\)-Poisson and \(n\)-Sklyanin brackets (English)
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12 September 2002
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It was proved independently by many authors that \(n\)-Poisson brackets, locally, are Jacobians on some subset of variables. The author presents the proof of this theorem obtained him in [Vestn. Samar. Gos. Univ., Mat. Mekh. Fiz. Khim. Biol. 1996, No.2, 33--41 (1996; Zbl 0986.37048)]. He also considers the notion of \(n\)-Sklyanin brackets and gives without proof a theorem on their symplectic leaves and Casimir functions.
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\(n\)-Lie algebra
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Filippov algebra
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\(n\)-Poisson bracket
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\(n\)-Sklyanin bracket
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symplectic leaf
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Casimir function
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0.9239918
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0.9151154
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0.9150727
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0.9077478
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0.8948791
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0.8927658
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