# The Ext-Algebra for infinitesimal deformations

Let \(f\) be a Hochschild \(2\)-cocycle and \(A_f\) an infinitesimal deformation of a finite-dimensional associative \(k\)-algebra \(A\). We describe, under some conditions on \(f\), the algebra structure of the Ext-algebra of \(A_f\) in terms of the Ext-algebra of \(A\). We achieve this description by getting an explicit construction of minimal projective resolutions. This is based on joint work with L. Román and F. Rossi Bertone.