Quantum dynamical Yang-Baxter equation over a nonabelian base

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21 Scopus citations

Abstract

In this paper we consider dynamical r-matrices over a nonabelian base. There are two main results. First, corresponding to a fat reductive decomposition of a Lie algebra g = h ⊕ m, we construct geometrically a non-degenerate triangular dynamical r-matrix using symplectic fibrations. Second, we prove that a triangular dynamical r-matrix r : h* → Λ2g naturally corresponds to a Poisson manifold h* × G. A special type of quantization of this Poisson manifold, called compatible star products in this paper, yields a generalized version of the quantum dynamical Yang-Baxter equation (or Gervais-Neveu-Felder equation). As a result, the quantization problem of a general dynamical r-matrix is proposed.

Original languageEnglish (US)
Pages (from-to)475-495
Number of pages21
JournalCommunications In Mathematical Physics
Volume226
Issue number3
DOIs
StatePublished - Apr 1 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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