Quantization of symplectic dynamical r-matrices and the quantum composition formula

Details Quantization of symplectic dynamical r-matrices and the quantum composition formula Quantization of symplectic dynamical r-matrices and the quantum composition formula

2006-06-20

arxiv.org/abs/math/0606498v3

Comm. Math. Phys. 273 (2007), no. 1, 119-136

Mathematics

Quantum Algebra

15 pages, final version, appeared in CMP

Scientific paper

10.1007/s00220-007-0245-z

In this paper we quantize symplectic dynamical r-matrices over a possibly nonabelian base. The proof is based on the fact that the existence of a star-product with a nice property (called strong invariance) is sufficient for the existence of a quantization. We also classify such quantizations and prove a quantum analogue of the classical composition formula for coboundary dynamical r-matrices.

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