Tuesday, February 4, 14:00, 7.527
Chrysostomos Psaroudakis (Ioannina), Gorenstein algebras, singular
equivalences and the Fg condition for Hochschild cohomology.
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