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

TL;DR

This paper investigates the algebraic properties of etale groupoid algebras, focusing on simplicity, primitivity, and semiprimitivity, with applications to inverse semigroup algebras and Leavitt path algebras.

Contribution

It provides new criteria and results for the simplicity, primitivity, and semiprimitivity of etale groupoid algebras, extending to inverse semigroup and Leavitt path algebras.

Findings

Recovered semiprimitivity of Leavitt path algebras

Established criteria for primitivity of Leavitt path algebras

Analyzed simplicity and semiprimitivity conditions for etale groupoid algebras

Abstract

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to \'etale 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.