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Quantization of Alekseev-Meinrenken dynamical r-matrices | Benjamin Enriquez
; Pavel Etingof
; | Date: |
6 Feb 2003 | Subject: | Quantum Algebra | math.QA | 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. | Source: | arXiv, math.QA/0302067 | Services: | Forum | Review | PDF | Favorites |
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