The Ext-algebra for infinitesimal deformations

Abstract

Let f be a Hochschild 2-cocycle and let Af be an infinitesimal deformation of an associative finite dimensional algebra A over an algebraically closed field k. We investigate the algebra structure of the Ext-algebra of Af and, under some conditions on f, we describe it in terms of the Ext-algebra of A. We achieve this description by getting an explicit construction of minimal projective resolutions in mod Af .