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Quantization of some Poisson-Lie dynamical r-matrices and Poisson homogeneous spaces

B. Enriquez·P. Etingof·I. Marshall
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Abstract

Poisson-Lie (PL) dynamical r-matrices are generalizations of dynamical r-matrices, where the base is a Poisson-Lie group. We prove analogues of basic results for these r-matrices, namely constructions of (quasi)Poisson groupoids and of Poisson homogeneous spaces. We introduce a class of PL dynamical r-matrices, associated to nondegenerate Lie bialgebras with a splitting; this is a generalization of trigonometric r-matrices with an abelian base. We prove a composition theorem for PL dynamical r-matrices, and construct quantizations of the polarized PL dynamical r-matrices. This way, we obtain quantizations of Poisson homogeneous structures on G/L (G a semisimple Lie group, L a Levi subgroup), thereby generalizing earlier constructions.

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BibTeXRIS

B. Enriquez, P. Etingof, I. Marshall. 2004-06-14. Quantization of some Poisson-Lie dynamical r-matrices and Poisson homogeneous spaces. https://arxiv.org/abs/math/0403283

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