Deformations of monomial algebras

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

CIUDAD DE MEXICO

Congreso; Sesio ́n de Representaciones de Algebras del XXIII CLA Coloquio Latinoamericano de Algebra; 2019

Universidad de Mexico

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.