Noncommutative deformations of modules (Q1605649)

A non commutative deformation theory for modules on \(k\)-algebras is proposed and studied. First, the author introduces a deformation functor on the category of Artinian \(r\)-pointed not necessarily commutative \(k\)-algebras, generalizing the ordinary deformation functor as defined for instance by \textit{M. Schlessinger} [in Trans. Am. Math. Soc. 130, 208-222 (1968; Zbl 0167.49503)]. It is then proved that the generalized functor has a prorepresenting hull, which can be computed in terms of Ext-groups and their matric Massey products. A generalized Burnside theorem is then given. Finally, the general problem of classification of iterated extensions of a family of modules is studied and projects for forthcoming papers are described.