Morita invariance for infinitesimal deformations

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

Algebras and Representation Theory

SPRINGER

Lugar: Berlin; Año: 2021

1386-923X

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.