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2011•Journal of Xinjiang Normal UniversityRequires access

Properties of Poisson Affine Group

He Yong

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Abstract

Poisson manifold,which act as the phase space of the generalized Hamilton system,Based on the work by the period.In this paper,Lie Group is endued with Poisson structure,Definition of Poisson affine group and Poisson bracket are given,and the conclusion are proved that Poisson bracket satisfies bilinear try,antisymmetry,Leibniz principle and Jacobi identity.At the same time,some proposition about Poisson map and Poisson functions are discussed.

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Poisson manifold,which act as the phase space of the generalized Hamilton system,Based on the work by the period.In this paper,Lie Group is endued with Poisson structure,Definition of Poisson affine group and Poisson bracket are given,and the conclusion are proved that Poisson bracket satisfies bilinear try,antisymmetry,Leibniz principle and Jacobi identity.At the same time,some proposition about Poisson map and Poisson functions are discussed.

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Available abstract

Poisson manifold,which act as the phase space of the generalized Hamilton system,Based on the work by the period.In this paper,Lie Group is endued with Poisson structure,Definition of Poisson affine group and Poisson bracket are given,and the conclusion are proved that Poisson bracket satisfies bilinear try,antisymmetry,Leibniz principle and Jacobi identity.At the same time,some proposition about Poisson map and Poisson functions are discussed.

Key concepts: Poisson algebra, Poisson bracket, Poisson distribution, Mathematics, Jacobi identity, First class constraint, Poisson manifold, Group (periodic table)

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