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The Erwin Schroedinger Institute for Mathematical Physics

Catherine Meusburger (U Erlangen): Introduction to Poisson Lie-groups

Lecture I  March 27, 2017
Lecture II March 28, 2017
Lecture III March 29, 2017
Lecture IV March 31, 2017 


Abstract:
A Poisson-Lie group is a Lie group that is also a Poisson manifold in
such a way that the multiplication is a Poisson map.
On the Lie algebra level, this implies that the dual vector space of its
Lie algebra also has a Lie algebra structure, and the two Lie algebra
structures satisfy a compatibility condition.


This is called a Lie bialgebra and can be viewed as the infinitesimal
counterpart of a quantum group.  Hence, we can interpret Lie-bialgebras
as the infinitesimal counterparts and Poisson-Lie groups as the
classical counterparts  of quantum groups.

I explain these relations and then discuss Poisson actions of
Poisson-Lie groups on Poisson manifolds. I explain why these structures
can be expected to appear in gauge theory. If there is time, I also
cover Drinfeld's classification of Poisson homogeneous spaces, i.e.
Poisson manifolds with transitive Poisson actions of Poisson-Lie groups.

Flyer (pdf)

At a glance

Type: Lecture
When: Mar 27, 2017 to
Mar 31, 2017
Where: ESI, Boltzmann Lecture Hall
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