Brauer graph algebras, Coverings and Ext algebras
Nicole Snashall (U Leicester)
Wednesday 14th November, 2012 16:00-17:00 516
We start with a brief introduction to 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 introduce 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.