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arxiv: 1307.2047 · v2 · pith:I3BH6WXDnew · submitted 2013-07-08 · 🧮 math.QA · math.SG

On Deformation Quantization of Poisson-Lie Groups and Moduli Spaces of Flat Connections

classification 🧮 math.QA math.SG
keywords connectionsflatmoduliquantizationspacesdeformationdrinfegroups
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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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