Koszul algebras, generalisations and cohomology

Part of the pure mathematics algebra seminar series.

Koszul algebras occur in many areas of algebra and algebraic topology. A classical result is that the Ext algebra of a Koszul algebra is finitely generated as an algebra and is again a Koszul algebra. We discuss several generalisations of Koszul algebras and introduce a more general class of graded algebras, called (D,A)-stacked algebras. Here we show that the Ext algebra is finitely generated and give a regrading on the Ext algebra so that the regraded algebra is again a Koszul algebra. We also discuss applications to the Hochschild cohomology ring.

The final part of the talk considers the Ext algebra of a Brauer graph algebra (BGA), where we classify the Koszul BGAs. BGAs play a major role in the classification of finite-dimensional self-injective algebras of tame representation type, in addition to the role of Brauer tree algebras in studying blocks of group algebras with cyclic defect groups.

This talk is based on several joint papers.

After each talk at 4:15pm there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber.