Chrysostomos Psaroudakis (Ioannina), Gorenstein algebras, singular equivalences and the Fg condition for Hochschild cohomology.

Abstract:

Support varieties for finite dimensional algebras were introduced by Snashall-Solberg using the Hochschild cohomology ring. Many results concerning support varieties are only valid if the algebra satisfies certain finite generation conditions, called Fg, and moreover when Fg holds then the algebra is Gorenstein. Given an Artin algebra A and an idempotent element a, our aim is to present a common context where we can compare the algebras A and aAa, with respect to Gorensteinness, singular equivalence and the Fg condition for Hochschild cohomology. In particular, under some conditions on the idempotent element a, we show that A is Gorenstein if and only if aAa is Gorenstein, the singularity categories of A and aAa are equivalent and that A satisfies Fg if and only if the algebra aAa satisfies Fg.

This talk is based on joint work with Oystein Skartsaeterhagen and Oyvind Solberg.