On $(σ,τ)$-derivations of group algebra as category characters

Abstract

For the space of (σ , τ)-derivations of the group algebra C[G] of a discrete countable group G, the decomposition theorem for the space of (σ , τ)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several corollaries and examples describing when all (σ , τ)-derivations are inner are obtained. Considered in details cases on (σ , τ)−nilpotent groups and (σ , τ)−FC groups.

$(σ, τ)$-Derivations of Group Algebras

“…These derivations have been principally used in solving functional equations [5]. For more applications of (σ, τ )-derivations, we refer the reader to [1]. Derivations, and especially (σ, τ )-derivations of group rings have various applications in coding theory [4], [7].…”