Poisson Lie group structures on real
semi-simple Lie groups
Alan
Shek Hei CHOW
Abstract
A Poisson Lie group is a Lie group G with a compatible Poisson structure. In
this talk, I will recall the correspondences between simply connected Poisson
Lie groups, Lie biaglebras, and Manin
triples. Let g be a complex semi-simple Lie algebra. We show that
for any real form g0 of y, there exists a real Lie subalgebra l such that ( g, g0, l ) is a Manin triple. We
also show that the Manin triple ( g, g0, l ) is coboundary
for g0 and we
compute its r-matrix. Thus every
connected Lie group G0
with Lie algebra g0 is a non-trivial Poisson Lie group. If time
permits, we will show some examples of Poisson homogeneous spaces of G0.
Date: |
October 14, 2004 (Thursday) |
Time: |
|
Place: |
Room 517, Meng
Wah Complex |
All are welcome