Quadratic Poisson structures and Nambu mechanics

Partha Guha

doi:10.1016/j.na.2005.11.051

Quadratic Poisson structures and Nambu mechanics

Partha Guha

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study a special class of Poisson structures, namely quadratic Poisson structures, on Rⁿ which contains the celebrated Sklyanin algebras which play the significant role in the theory of exactly solvable models of classical and quantum systems. In this paper we study such quadratic Poisson structures via Nambu mechanics.

Original language	British English
Pages (from-to)	2025-2034
Number of pages	10
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	65
Issue number	11
DOIs	https://doi.org/10.1016/j.na.2005.11.051
State	Published - 1 Dec 2006

Keywords

Casimir
Nambu mechanics
Poisson structure
Sklyanin algebra

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10.1016/j.na.2005.11.051

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abstract = "We study a special class of Poisson structures, namely quadratic Poisson structures, on Rn which contains the celebrated Sklyanin algebras which play the significant role in the theory of exactly solvable models of classical and quantum systems. In this paper we study such quadratic Poisson structures via Nambu mechanics.",

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AB - We study a special class of Poisson structures, namely quadratic Poisson structures, on Rn which contains the celebrated Sklyanin algebras which play the significant role in the theory of exactly solvable models of classical and quantum systems. In this paper we study such quadratic Poisson structures via Nambu mechanics.

KW - Casimir

KW - Nambu mechanics

KW - Poisson structure

KW - Sklyanin algebra

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Quadratic Poisson structures and Nambu mechanics

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Keywords

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