Lie groups in quasi-Poisson geometry and braided Hopf algebras

TL;DR

This paper generalizes Poisson-Lie groups to g-quasi-Poisson geometry, introduces their quantization into braided Hopf algebras, and provides examples from nilpotent radicals and moduli spaces.

Contribution

It extends the theory of Poisson-Lie groups to a broader g-quasi-Poisson setting and constructs their quantization as braided Hopf algebras.

Findings

Introduction of g-quasi-Poisson Lie groups

Quantization into braided Hopf algebras in Drinfeld category

Examples from nilpotent radicals and moduli spaces

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.