Lie Groups in Quasi-Poisson Geometry and Braided Hopf Algebras

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.

2010 Mathematics Subject Classification: 53D17, 16T05, 53D55

Keywords and Phrases:

Full text: dvi.gz 45 k, dvi 158 k, ps.gz 321 k, pdf 212 k.

Home Page of DOCUMENTA MATHEMATICA