English

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.

Keywords

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}
}

Comments

11 pages