Finite generation for Hochschild cohomology of Gorenstein monomial algebras

Abstract

We show that a finite dimensional monomial algebra satisfies the finite generation conditions of Snashall-Solberg for Hochschild cohomology if and only if it is Gorenstein. This gives, in the case of monomial algebras, the converse to a theorem of Erdmann-Holloway-Snashall-Solberg-Taillefer. We also give a necessary and sufficient combinatorial criterion for finite generation.

38 pages, comments are welcome

References in corpus (3)

• Support varieties for selfinjective algebras
• The A-infinity Centre of the Yoneda Algebra and the Characteristic Action of Hochschild Cohomology on the Derived Category
• Free resolutions of algebras

Cited by in corpus (2)

• Periodic dimensions and some homological properties of eventually periodic algebras
• A combinatorial characterisation of d-Koszul and (D,A)-stacked monomial algebras that satisfy (Fg)