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

2014/08/26 by Benjamin Steinberg, Steinberg, Benjamin · 2 citations
Computer Science · Mathematics · #16S36 #16S99 #18F20 #20M18 #20M25 #22A22 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.CT #math.GR #math.OA #math.RA #math.RT #msc:16S36 #msc:16S99 #msc:18F20 #msc:20M18 #msc:20M25 #msc:22A22

paper · pdf · doi:10.48550/arxiv.1408.6014

Updated after referee report and corrected misprints

openalex publication_date 2014/08/26 · arxiv created 2015/06/25 · arxiv updated 2015/06/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

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.

Cited by

• Operator algebras over the p-adic integers -- II
• Complexity and recurrence in infinite words and related structures

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