Semigroups of self-similar actions and higher rank Baumslag-Solitar semigroups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915255575117824 |
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| author | Valente, Robert Yang, Dilian |
| author_facet | Valente, Robert Yang, Dilian |
| contents | In this paper, we initiate the study of higher rank Baumslag-Solitar semigroups and their related C*-algebras. We focus on two extreme, but interesting, classes - one is related to products of odometers and the other is related to Furstenberg's $\times p,, \times q$ conjecture. For the former class, whose C*-algebras are studied by H. Li and the second author, we here characterize the factoriality of the associated von Neumann algebras and further determine their types; for the latter, we obtain their canonical Cartan subalgebras. In the rank 1 case, we study a more general setting which encompasses (single-vertex) generalized Baumslag-Solitar semigroups. One of our main tools is from self-similar higher rank graphs and their C*-algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_07062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semigroups of self-similar actions and higher rank Baumslag-Solitar semigroups Valente, Robert Yang, Dilian Operator Algebras Functional Analysis In this paper, we initiate the study of higher rank Baumslag-Solitar semigroups and their related C*-algebras. We focus on two extreme, but interesting, classes - one is related to products of odometers and the other is related to Furstenberg's $\times p,, \times q$ conjecture. For the former class, whose C*-algebras are studied by H. Li and the second author, we here characterize the factoriality of the associated von Neumann algebras and further determine their types; for the latter, we obtain their canonical Cartan subalgebras. In the rank 1 case, we study a more general setting which encompasses (single-vertex) generalized Baumslag-Solitar semigroups. One of our main tools is from self-similar higher rank graphs and their C*-algebras. |
| title | Semigroups of self-similar actions and higher rank Baumslag-Solitar semigroups |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2405.07062 |