Quantization of classical dynamical $r$-matrices with nonabelian base

Details Quantization of classical dynamical $r$-matrices with nonabelian base Quantization of classical dynamical $r$-matrices with nonabelian base

2003-11-13

arxiv.org/abs/math/0311224v2

Mathematics

Quantum Algebra

40 pages; added references; corrected critical cocycle

Scientific paper

We construct some classes of dynamical $r$-matrices over a nonabelian base, and quantize some of them by constructing dynamical (pseudo)twists in the sense of Xu. This way, we obtain quantizations of $r$-matrices obtained in earlier work of the second author with Schiffmann and Varchenko. A part of our construction may be viewed as a generalization of the Donin-Mudrov nonabelian fusion construction. We apply these results to the construction of equivariant star-products on Poisson homogeneous spaces, which include some homogeneous spaces introduced by De Concini.

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