Quantization of Alekseev-Meinrenken dynamical r-matrices

2003/02/06 by Benjamin Enriquez, Pavel Etingof, Enriquez, Benjamin +1 · 1 citation
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0302067

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

arxiv created 2003/03/01 · arxiv updated 2009/11/30

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 S²(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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• Brace B_∞ algebras associated with Hopf algebroids

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