Poisson Manifolds Associated with Group Actions and Classical Triangular r-Matrices

Ping Xu

doi:10.1006/jfan.1993.1031

Poisson Manifolds Associated with Group Actions and Classical Triangular r-Matrices

Ping Xu

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

9 Scopus citations

Abstract

Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure P_Λ on P. For this new Poisson structure P_Λ, we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of P_Λ is also discussed.

Original language	English (US)
Pages (from-to)	218-240
Number of pages	23
Journal	Journal of Functional Analysis
Volume	112
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1993.1031
State	Published - Feb 15 1993

All Science Journal Classification (ASJC) codes

Analysis

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10.1006/jfan.1993.1031

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title = "Poisson Manifolds Associated with Group Actions and Classical Triangular r-Matrices",

abstract = "Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure PΛ on P. For this new Poisson structure PΛ, we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of PΛ is also discussed.",

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N2 - Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure PΛ on P. For this new Poisson structure PΛ, we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of PΛ is also discussed.

AB - Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure PΛ on P. For this new Poisson structure PΛ, we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of PΛ is also discussed.

UR - https://www.scopus.com/pages/publications/22244488802

UR - https://www.scopus.com/pages/publications/22244488802#tab=citedBy

U2 - 10.1006/jfan.1993.1031

DO - 10.1006/jfan.1993.1031

M3 - Article

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VL - 112

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EP - 240

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Poisson Manifolds Associated with Group Actions and Classical Triangular r-Matrices

Abstract

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