Dynamical Yang-Baxter equations, quasi-Poisson homogeneous spaces, and quantization

Details Dynamical Yang-Baxter equations, quasi-Poisson homogeneous spaces, and quantization Dynamical Yang-Baxter equations, quasi-Poisson homogeneous spaces, and quantization

2003-09-11

arxiv.org/abs/math/0309203v3

Mathematics

Quantum Algebra

18 pages, a new section added

Scientific paper

This paper is a continuation of [KS]. We develop the results of [KS] principally in two directions. First, we generalize the main result of [KS], the connection between the solutions of the classical dynamical Yang-Baxter equation and Poisson homogeneous spaces of Poisson Lie groups. We hope that now we present this result in its natural generality. Secondly, we propose a partial quantization of the results of [KS]. [KS] E. Karolinsky and A. Stolin, Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras, Lett. Math. Phys., 60 (2002), p.257-274; e-print math.QA/0110319.

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