Derivations for a Special Case of Inverse Semigroup Algebras

Abstract

This paper is aimed at studying the derivations of inverse semigroups algebras. We adress a special case of semigroups which are constructed as a disjoint union of two groups. We use a categorical method, constructing a category and expressing the derivations in terms of characters on said category. The resulting derivation algebra is proven to be divisible into direct sum of derivation algebras for two groups.