A correspondence between inverse subsemigroups, open wide subgroupoids and Cartan intermediate C*-subalgebras
Operator Algebras
2020-07-23 v1 Group Theory
Abstract
For a given inverse semigroup action on a topological space, one can associate an \'etale 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.
Keywords
Cite
@article{arxiv.2007.11456,
title = {A correspondence between inverse subsemigroups, open wide subgroupoids and Cartan intermediate C*-subalgebras},
author = {Fuyuta Komura},
journal= {arXiv preprint arXiv:2007.11456},
year = {2020}
}
Comments
18 pages