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Lie groups in quasi-Poisson geometry and braided Hopf algebras (1604.07164v2)
Published 25 Apr 2016 in math.SG and math.QA
Abstract: We extend the notion of Poisson-Lie groups and Lie bialgebras from Poisson to g-quasi-Poisson geometry and provide a quantization to braided Hopf algebras in the corresponding Drinfeld category. The basic examples of these g-quasi-Poisson Lie groups are nilpotent radicals of parabolic subgroups. We also provide examples of moment maps in this new context coming from moduli spaces of flat connections on surfaces.