A correspondence between inverse subsemigroups, open wide subgroupoids and Cartan intermediate C*-subalgebras

2020/07/22 by Fuyuta Komura, Komura, Fuyuta
Mathematics · #20M18 #22A22 #46L05 #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #math.GR #math.OA #msc:20M18 #msc:22A22 #msc:46L05

paper · pdf · doi:10.48550/arxiv.2007.11456

18 pages

arxiv created 2020/07/22 · arxiv updated 2020/07/23

Abstract

For a given inverse semigroup action on a topological space, one can associate an étale groupoid. We prove that there exists a correspondence between the certain subsemigroups and the open wide subgroupoids in case that the action is strongly tight. Combining with the recent result of Brown et. al, we obtain a correspondence between the certain subsemigroups of an inverse semigroup and the Cartan intermediate subalgebras of a groupoid C*-algebra.

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