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 ?=?⊕?, we construct geometrically a non-degenerate triangular dynamical r-matrix using symplectic fibrations. Second, we prove that a triangular dynamical r-matrix naturally corresponds to a Poisson manifold ?⋆×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.
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Received: 19 May 2001 / Accepted: 19 November 2001
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Xu, P. Quantum Dynamical Yang–Baxter Equation¶Over a Nonabelian Base. Commun. Math. Phys. 226, 475–495 (2002). https://doi.org/10.1007/s002200200621
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DOI: https://doi.org/10.1007/s002200200621