Embeddability of higher-rank graphs in groupoids, and the structure of their C*-algebras
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911787966791680 |
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| author | Brownlowe, Nathan Kumjian, Alex Pask, David Sims, Aidan |
| author_facet | Brownlowe, Nathan Kumjian, Alex Pask, David Sims, Aidan |
| contents | We show that the C*-algebra of a row-finite source-free k-graph is Rieffel-Morita equivalent to a crossed product of an AF algebra by the fundamental group of the k-graph. When the k-graph embeds in its fundamental groupoid, this AF algebra is a Fell algebra; and simple-connectedness of a certain sub-1-graph characterises when this Fell algebra is Rieffel--Morita equivalent to a commutative C*-algebra. We provide a substantial suite of results for determining if a given k-graph embeds in its fundamental groupoid, and provide a large class of examples, arising via work of Cartwright, Robertson, Steger et al. from the theory of $\tilde{A_2}$-groups, that do embed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embeddability of higher-rank graphs in groupoids, and the structure of their C*-algebras Brownlowe, Nathan Kumjian, Alex Pask, David Sims, Aidan Operator Algebras 46L05 (primary), 18D99 (secondary) We show that the C*-algebra of a row-finite source-free k-graph is Rieffel-Morita equivalent to a crossed product of an AF algebra by the fundamental group of the k-graph. When the k-graph embeds in its fundamental groupoid, this AF algebra is a Fell algebra; and simple-connectedness of a certain sub-1-graph characterises when this Fell algebra is Rieffel--Morita equivalent to a commutative C*-algebra. We provide a substantial suite of results for determining if a given k-graph embeds in its fundamental groupoid, and provide a large class of examples, arising via work of Cartwright, Robertson, Steger et al. from the theory of $\tilde{A_2}$-groups, that do embed. |
| title | Embeddability of higher-rank graphs in groupoids, and the structure of their C*-algebras |
| topic | Operator Algebras 46L05 (primary), 18D99 (secondary) |
| url | https://arxiv.org/abs/2403.01337 |