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Quantization of Alekseev-Meinrenken dynamical r-matrices

Benjamin Enriquez·Pavel Etingof
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Abstract

We quantize the Alekseev-Meinrenken solution r to the classical dynamical Yang-Baxter equation, associated to a Lie algebra g with an element t in S^2(g)^g. Namely, we construct a dynamical twist J with nonabelian base in the sense of P. Xu, whose quasiclassical limit is r-t/2. This twist gives rise to a dynamical quantum R-matrix, and also provides a quantization of the quasi-Poisson manifold and Poisson groupoid associated to r. The twist J is obtained by an appropriate renormalization of the Knizhnik-Zamolodchikov associator for g, introduced by Drinfeld.

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Benjamin Enriquez, Pavel Etingof. 2003-03-01. Quantization of Alekseev-Meinrenken dynamical r-matrices. https://arxiv.org/abs/math/0302067

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