MODULES WITH VALUES IN THE SPACE OF ALL DERIVATIONS OF AN ALGEBRA

Abstract

In this paper, we construct a groupoid associated to a modulewith values in the space of all derivations of a unital algebra. More precisely,for a pair (A, G) consisting of an algebra A with a unit, a module G over thecenter Z(A) of A together with a homomorphism of Z(A)-modules from G tothe space of all derivations Der(A) of A, we associate a groupoid. We discusson the equivalence relation induced from this groupoid