Quotients of the Booleanization of an inverse semigroup
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916455470071808 |
|---|---|
| author | Kudryavtseva, Ganna |
| author_facet | Kudryavtseva, Ganna |
| contents | 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-Szép product right LCM semigroup by Brownlowe, Ramagge, Robertson and Whittaker. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_14890 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quotients of the Booleanization of an inverse semigroup Kudryavtseva, Ganna Rings and Algebras Operator Algebras 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-Szép product right LCM semigroup by Brownlowe, Ramagge, Robertson and Whittaker. |
| title | Quotients of the Booleanization of an inverse semigroup |
| topic | Rings and Algebras Operator Algebras |
| url | https://arxiv.org/abs/2007.14890 |