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Brauer graph algebras, Coverings and Ext algebras
Wed 06 February 2013, 14:30
Nicole Snashall
University of Leicester
Organisers: Tony Skyner, Neil Saunders
ABSTRACT
This talk is based on research motivated by the study of Koszul algebras
and the question of finite generation of the Ext algebra of a finite
dimensional algebra.
We begin with a short introduction to these questions and then move on to
describe Brauer graph algebras. These are generalizations of Brauer tree
algebras, which were used, for group algebras KG over a finite group G, to
study blocks with cyclic defect groups. Brauer graph algebras have since
played a major role in the classification of finite-dimensional
self-injective algebras of tame representation type.
In recent joint work (with Green and Schroll), we introduced coverings of
Brauer graphs which are compatible with coverings of Brauer graph
algebras, and thus are able to classify the coverings of Brauer graph
algebras that are again Brauer graph algebras. Moreover, we show that
there is a tower of coverings so that any Brauer graph can be covered by a
Brauer graph that has multiplicity function precisely 1, no loops and no
multiple edges.
We then use this theory to compute the Ext algebra of a Brauer graph
algebra. This is joint with Green, Schroll and Taillefer. In particular,
we determine the Koszul Brauer graph algebras.