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

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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.

Original languageEnglish (US)
Pages (from-to)218-240
Number of pages23
JournalJournal of Functional Analysis
Volume112
Issue number1
DOIs
StatePublished - Feb 15 1993

All Science Journal Classification (ASJC) codes

  • Analysis

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