Quantum dynamical Yang-Baxter equation over a nonAbelian base
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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 \frakg =\frakh \oplus \frakm, we construct geometrically a non-degenerate triangular dynamical r-matrix using symplectic fibrations. Second, we prove that a triangular dynamical r-matrix r: \frakh^* \lon \wedge^2 \frakg corresponds to a Poisson manifold \frakh^* \times G. A special type of quantizations 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.Note:
- 23 pages, minor changes made, final version to appear in Comm. Math. Phys
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