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

Part of: Semigroups Selfadjoint operator algebras Topological and differentiable algebraic systems

Published online by Cambridge University Press:  07 October 2022

Fuyuta Komura Open the ORCID record for Fuyuta Komura [Opens in a new window]
Fuyuta Komura*
Affiliation:
Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan ([email protected])
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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.

Keywords

C*-algebrasétale groupoidsinverse semigroups

MSC classification

Primary: 20M18: Inverse semigroups 22A22: Topological groupoids (including differentiable and Lie groupoids) 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 3 , August 2022 , pp. 861 - 879
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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References

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