University of Birmingham > Talks@bham > Algebra Seminar > Generalisations of Koszul algebras and the Ext algebra

Generalisations of Koszul algebras and the Ext algebra

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If you have a question about this talk, please contact Anton Evseev.

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. 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 then consider Brauer graph algebras and classify those which are Koszul, as well as giving more general results on the Ext algebra of a Brauer graph algebra. Brauer graph algebras 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 joint work with J Leader, and with EL Green, S Schroll and R Taillefer.

This talk is part of the Algebra Seminar series.

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