On Deformation Quantization of Poisson-Lie Groups and Moduli Spaces of Flat Connections
Quantum Algebra
2014-09-26 v2 Symplectic Geometry
Abstract
We give simple explicit formulas for deformation quantization of Poisson-Lie groups and of similar Poisson manifolds which can be represented as moduli spaces of flat connections on surfaces. The star products depend on a choice of Drinfe\v{l}d associator and are obtained by applying certain monoidal functors (fusion and reduction) to commutative algebras in Drinfe\v{l}d categories. From a geometric point of view this construction can be understood as a quantization of the quasi-Poisson structures on moduli spaces of flat connections.
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Cite
@article{arxiv.1307.2047,
title = {On Deformation Quantization of Poisson-Lie Groups and Moduli Spaces of Flat Connections},
author = {David Li-Bland and Pavol Ševera},
journal= {arXiv preprint arXiv:1307.2047},
year = {2014}
}
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11 pages