The Hochschild cohomology ring of monomial path algebras

Dalia Artenstein, Janina C. Letz, Amrei Oswald, Andrea Solotar

Published 2023-12-22Version 1

We give an explicit description of a diagonal map on the Bardzell resolution for any monomial path algebra, and we use this diagonal map to describe the cup product on Hochschild cohomology. Then, we prove that the cup product is trivial in positive degrees for triangular monomial path algebras. Our proof uses the graded-commutativity of the cup product on Hochschild cohomology and does not rely on explicit computation of the Hochschild cohomology modules.