Resumen de Finite generation for Hochschild cohomology of Gorenstein monomial algebras

Vladimir Dotsenko, Vincent Gélinas, Pedro Tamaroff

• 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.