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University of Sydney Algebra Seminar

Vera Serganova

Friday 23 June, 12-1pm, Place: Carslaw 157-257

A root groupoid is Coxeter

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.