C*-Algebras of one-sided subshifts over arbitrary alphabets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929195156766720 |
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| author | Boava, Giuliano de Castro, Gilles G. Gonçalves, Daniel van Wyk, Daniel W. |
| author_facet | Boava, Giuliano de Castro, Gilles G. Gonçalves, Daniel van Wyk, Daniel W. |
| contents | We associate a C*-algebra $\widetilde{\mathcal{O}}_{\textsf{X}}$ with a subshift over an arbitrary, possibly infinite, alphabet. We show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is a full invariant for topological conjugacy of the subshifts of Ott, Tomforde, and Willis. When the alphabet is countable, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is an invariant for isometric conjugacy of subshifts with the product metric. For a suitable partial action associated with a subshift over a countable alphabet, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is also an invariant for continuous orbit equivalence. Additionally, we give a concrete way to compute the K-theory of $\widetilde{\mathcal{O}}_{\textsf{X}}$ and illustrate it with two examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17644 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | C*-Algebras of one-sided subshifts over arbitrary alphabets Boava, Giuliano de Castro, Gilles G. Gonçalves, Daniel van Wyk, Daniel W. Operator Algebras Dynamical Systems Rings and Algebras We associate a C*-algebra $\widetilde{\mathcal{O}}_{\textsf{X}}$ with a subshift over an arbitrary, possibly infinite, alphabet. We show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is a full invariant for topological conjugacy of the subshifts of Ott, Tomforde, and Willis. When the alphabet is countable, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is an invariant for isometric conjugacy of subshifts with the product metric. For a suitable partial action associated with a subshift over a countable alphabet, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is also an invariant for continuous orbit equivalence. Additionally, we give a concrete way to compute the K-theory of $\widetilde{\mathcal{O}}_{\textsf{X}}$ and illustrate it with two examples. |
| title | C*-Algebras of one-sided subshifts over arbitrary alphabets |
| topic | Operator Algebras Dynamical Systems Rings and Algebras |
| url | https://arxiv.org/abs/2312.17644 |