Quantization of Alekseev-Meinrenken dynamical r-matrices
Quantum Algebra
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0302067,
title = {Quantization of Alekseev-Meinrenken dynamical r-matrices},
author = {Benjamin Enriquez and Pavel Etingof},
journal= {arXiv preprint arXiv:math/0302067},
year = {2007}
}
Comments
15 pages, latex; in the new version the results were extended to the case of Lie algebras with an invariant element in the third exterior power