Deformations of monomial algebras

REDONDO, MARIA JULIA; ROMAN, LUCRECIA; FIORELA ROSSI BERTONE; MELINA VERDECCHIA

Saint Petersburg

Congreso; Homological algebra, ring theory and Hochschild cohomology, dedicated to the 70th birthday of Alexander Generalov; 2019

The Euler International Mathematical Institute

Let A and B be two Morita equivalent finite dimensional associative algebras overa field k. It is well known that Hochschild cohomology is invariant under Morita equivalence.Since infinitesimal deformations are connected with the second Hochschild cohomology group,we explicitly describe the transfer map connecting HH2(A) with HH2(B). This allows us totransfer Morita equivalence between A and B to that between infinitesimal deformations ofthem. As an application, when k is algebraically closed, we consider the quotient path algebra associated to A and describe the presentation by quiver and relations of the infinitesimaldeformations of A.