On $(\sigma,\tau)$-derivations of group algebra as category characters

Abstract

For the space of $(\sigma,\tau)$-derivations of the group algebra $ \mathbb{C} [G] $ of discrete countable group $G$, the decomposition theorem for the space of $(\sigma,\tau)$-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 $(\sigma,\tau)$-derivations are inner are obtained. Considered in details cases on $(\sigma,\tau)-$nilpotent groups and $(\sigma,\tau)$-$FC$ groups.