Combinatorial Description of Derivations in Group Algebras

The work is devoted to the study of derivations in group algebras using the results of combinatorial group theory. A survey of old results is given, describing derivations in group algebras as characters on an adjoint action groupoid. In this paper, new assertions are presented that make it possible to connect derivations of group algebras with the theory of ends of groups and in particular the Stallings theorem. A homological interpretation of the results obtained is also given. We also construct a generalization of the proposed construction for the case of modules over a group ring.