Algebra Seminar: Serganova -- A root groupoid is Coxeter

Vera Serganova (UC Berkeley) is speaking in the Algebra Seminar this week.  Note that we
will meet in Carslaw 157-257, unlike usual.  We will go out for lunch after the talk.  

When: Friday 23 June, 12-1pm 

Where: Carslaw 157-257 

Title: A root groupoid is Coxeter 

Abstract: Motivated by the theory of Kac-Moody superalgebras we introduce a notion of
root groupoid associated with given root data.This definition can be considered as a
generalization of the Weyl group to the supercase.  Even in the non-supercase case the
groupoid approach gives a nice way to obtain Serre’s relations for Kac-Moody algebras.
We also define the skeleton of a root groupoid, which generalizes the Cayley graph of a
Coxeter group and prove that the skeleton is Coxeter in the natural sense.  The main
part of the proof involves interesting convex polytopes.  This is a joint work with M.
Gorelik and V.  Hinich.