Singular Hochschild Cohomology of Radical Square Zero Algebras

Zhengfang Wang

Published 2015-11-26Version 1

Following the approach developed by Cibils and S\'{a}nchez for ordinary Hochschild cohomology, we compute the singular Hochschild cohomology of radical square zero algebras. We show that the singular Hochschild cohomology of radical square zero algebras has a very combinatorial structure. A PROP interpretation for the Gerstenhaber bracket is given in the case of radical square zero algebras. This interpretation allows us to completely determine the Gerstenhaber algebra structures for several examples.