Boundary quotients of C$^*$-algebras of left cancellative monoids and their groupoid models
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908448855162880 |
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| author | Schwartz, Gaute |
| author_facet | Schwartz, Gaute |
| contents | For a left cancellative monoid $S$ we consider a quotient of the reduced semigroup C$^*$-algebra $C_r^*(S)$ known as the boundary quotient. We present two potential groupoid models for this boundary quotient, obtained as reductions of Paterson and Spielberg's groupoids associated to $S$, and formulate conditions on $S$ which guarantees that either is a groupoid model. We outline how these conditions are related to the notions (strong) C$^*$-regularity introduced in a previous paper, and construct an example of a left cancellative monoid which is not C$^*$-regular, but satisfies both of the new conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary quotients of C$^*$-algebras of left cancellative monoids and their groupoid models Schwartz, Gaute Operator Algebras For a left cancellative monoid $S$ we consider a quotient of the reduced semigroup C$^*$-algebra $C_r^*(S)$ known as the boundary quotient. We present two potential groupoid models for this boundary quotient, obtained as reductions of Paterson and Spielberg's groupoids associated to $S$, and formulate conditions on $S$ which guarantees that either is a groupoid model. We outline how these conditions are related to the notions (strong) C$^*$-regularity introduced in a previous paper, and construct an example of a left cancellative monoid which is not C$^*$-regular, but satisfies both of the new conditions. |
| title | Boundary quotients of C$^*$-algebras of left cancellative monoids and their groupoid models |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2507.10168 |