EMS Meeting: Koszul algebras, cohomology and support varieties
Professor Nicole Snashall (University of Leicester)
Friday 23rd March, 2018 16:00-17:00 Maths 311B
Koszul algebras occur in many areas of algebra and algebraic topology, and we start by introducing these algebras. We then classify the Koszul Brauer graph algebras, noting that Brauer graph algebras form an important class of self-injective algebras and include Brauer tree algebras (which arise in the study of blocks of group algebras with cyclic defect group). It is a classical result that the Ext algebra of a Koszul algebra is finitely generated as an algebra, and we discuss the relationship between the Ext algebra and the Hochschild cohomology ring of a Koszul algebra. This leads us to the theory of support varieties constructed via the Hochschild cohomology ring for modules over a finite-dimensional algebra. We give an overview of the theory and its applications, and discuss some recent work in this area. This talk is based on joint work from several papers.