A cohomological proof of Peterson-Kac's theorem on conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras
Speaker:
Uladzimir Yahorau, University of Alberta
Date and Time:
Thursday, March 7, 2013 - 1:30pm to 2:30pm
Location:
Fields Institute, Stewart Library
Abstract:
We say that a subalgebra of a Lie algebra is Cartan if it is ad-diagonalizable and not properly contained in a larger ad-diagonalizable subalgebra. The theorem of Peterson and Kac says that Cartan subalgebras of symmetrizable Kac-Moody Lie algebras are conjugate. We will discuss the proof of this theorem for affine Kac-Moody Lie algebras. Unlike the methods of Peterson and Kac, our approach is entirely cohomological and geometric.
This is a joint project with Vladimir Chernousov, Philippe Gille and Arturo Pianzola.
