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arXiv · 2007.14890

Quotients of the Booleanization of an inverse semigroup

Ganna Kudryavtseva
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Abstract

We introduce $X$-to-join representations of inverse semigroups which are a relaxation of the notion of a cover-to-join representation. We construct the universal $X$-to-join Booleanization of an inverse semigroup $S$ as a weakly meet-preserving quotient of the universal Booleanization ${\mathrm B}(S)$ and show that all such quotients of ${\mathrm B}(S)$ arise via $X$-to-join representaions. As an application, we provide groupoid models for the intermediate boundary quotients of the $C^*$-algebra of a Zappa-Sz\'ep product right LCM semigroup by Brownlowe, Ramagge, Robertson and Whittaker.

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Ganna Kudryavtseva. 2020-07-29. Quotients of the Booleanization of an inverse semigroup. https://doi.org/10.1007/978-981-33-4842-4_6

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