An introduction to noncommutative deformations of modules

Let k be an algebraically closed (commuitative) field, let A be an associative k-algebra, and let M = {M-1,..., M-p} be a finite family of left A-modules. We study the simultaneous formal deformations of this family, described by the noncommutative deformation functor Def(M) : a(p) -> Sets introduced in Laudal [8]. In particular, we prove that this deformation functor has a pro-representing hull, and describe how to calculate this hull using the cohomology groups Ext(A)(n)(M-i, M-j) and their matric Massey products.