The algebra of observables in noncommutative deformation theory
Abstract
We consider the algebra of observables and the (formally) versal morphism defined by the noncommutative deformation functor of a family of right modules over an associative k-algebra A. By the Generalized Burnside Theorem, due to Laudal, η is an isomorphism when A is finite dimensional, is the family of simple A-modules, and k is an algebraically closed field. The purpose of this paper is twofold: First, we prove a form of the Generalized Burnside Theorem that is more general, where there is no assumption on the field k. Secondly, we prove that the -construction is a closure operation when A is any finitely generated k-algebra and is any family of finite dimensional A-modules, in the sense that is an isomorphism when and is considered as a family of B-modules