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A correspondence between inverse subsemigroups, open wide subgroupoids and cartan intermediate C*-subalgebras
Published online by Cambridge University Press: 07 October 2022
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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 3 , August 2022 , pp. 861 - 879
- Copyright
- Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society