Simplicity, primitivity and semiprimitivity of étale groupoid algebras with applications to inverse semigroup algebras

Abstract

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to étale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and can be used to recover the known primitivity criterion for Leavitt path algebras.