Complex of n-categories and derivations in group algebras

Abstract

A description of the algebra of outer and inner derivations of a group algebra of a finitely presented discrete group is given in terms of the character spaces of the 2-groupoid of the adjoint action of the group.A certain generalization of this construction is considered, and also proposed a natural modification of the structure of internal and external derivations, which allows, taking into account the geometric constructions we introduce, to describe the algebra of derivations in some key examples of discrete finitely generated groups.