Geometry Seminar

 

 

Poisson Lie group structures on real

semi-simple Lie groups

 

Alan Shek Hei CHOW

The University of Hong Kong

 

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:

4:00 – 5:00pm

Place:

Room 517, Meng Wah Complex

 

 

All are welcome