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arXiv · 2007.11456

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

Fuyuta Komura
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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.

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Fuyuta Komura. 2020-07-22. A correspondence between inverse subsemigroups, open wide subgroupoids and Cartan intermediate C*-subalgebras. https://arxiv.org/abs/2007.11456

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