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

2003/09/11 by Eugene Karolinsky, Karolinsky, Eugene, Kolya Muzykin +5
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA) #math.DG #math.QA

paper · pdf · doi:10.48550/arxiv.math/0309203

18 pages, a new section added

openalex publication_date 2003/09/11 · arxiv created 2004/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Quasi-Poisson Manifolds

Related

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• Lectures on the dynamical Yang-Baxter equations