Place: TAU  Schreiber Mathematical Institute, room 309

Time: Tuesday,  12:10

Organizer: Evgeny Feigin  

Upcoming talks:

30.12.   Speaker: Vera Serganova (UC Berkeley)

Title: Root groupoid and Kac-Moody superalgebras  

Abstract:  It is well known that most simple Lie superalgebras has many non-isomorphic Borel subalgebras. As a consequence several Cartan matrices may define  the same Lie superalgera and there are many non-isomorphic flag supermanifolds. However, there is a way to connect non-conjugate Borel subalgebras containing the same maximal torus by

extending the Weyl group of the even part by so-called odd reflection. This extension has a natural groupoid structure.

We introduce a notion of root groupoid, such that connected components of this groupoid correspond to  Kac-Moody Lie superalgebras. Moreover, using this groupoid we describe Serre's relations. We also prove that the root groupoid is Coxeter, generalizing the fact that the Weyl group of a Kac-Moody Lie algebra is Coxeter. If time permits, I also review classification of Kac-Moody superalgebras of finite growth. Most of the talk is based on the joint work with M. Gorelik and V.Hinich. 

06.01. Avraham Aizenbud (WIS)

13.01. Boris Bychkov (UHaifa)

20.01. Inna Entova-Aizenbud (BGU)