Triangular dynamical r-matrices and quantization

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Abstract

We study some general aspects of triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix r: h* → ∧2 g always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate triangular dynamical r-matrices (i.e., those such that the corresponding Poisson manifolds are symplectic) are quantizable and that the quantization is classified by the relative Lie algebra cohomology H2(g, h) ℏ.

Original languageEnglish (US)
Pages (from-to)1-49
Number of pages49
JournalAdvances in Mathematics
Volume166
Issue number1
DOIs
StatePublished - Mar 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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