The reduction theorem for algebras of one-sided subshifts over arbitrary alphabets
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929255408992256 |
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| author | Bagio, Dirceu Canto, Cristóbal Gil Gonçalves, Daniel Royer, Danilo |
| author_facet | Bagio, Dirceu Canto, Cristóbal Gil Gonçalves, Daniel Royer, Danilo |
| contents | Let $R$ be a commutative unital ring, $\textsf{X}$ a subshift, and $\widetilde{\mathcal{A}}_R(\textsf{X})$ the corresponding unital subshift algebra. We establish the reduction theorem for $\widetilde{\mathcal{A}}_R(\textsf{X})$. As a consequence, we obtain a Cuntz-Krieger uniqueness theorem for $\widetilde{\mathcal{A}}_R(\textsf{X})$ and we show that $\widetilde{\mathcal{A}}_R(\textsf{X})$ is semiprimitive (resp. semiprime) whenever $R$ is a field (resp. a domain). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14983 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The reduction theorem for algebras of one-sided subshifts over arbitrary alphabets Bagio, Dirceu Canto, Cristóbal Gil Gonçalves, Daniel Royer, Danilo Rings and Algebras Dynamical Systems Operator Algebras 6S10, 16S88, 16N20, 16N60 Let $R$ be a commutative unital ring, $\textsf{X}$ a subshift, and $\widetilde{\mathcal{A}}_R(\textsf{X})$ the corresponding unital subshift algebra. We establish the reduction theorem for $\widetilde{\mathcal{A}}_R(\textsf{X})$. As a consequence, we obtain a Cuntz-Krieger uniqueness theorem for $\widetilde{\mathcal{A}}_R(\textsf{X})$ and we show that $\widetilde{\mathcal{A}}_R(\textsf{X})$ is semiprimitive (resp. semiprime) whenever $R$ is a field (resp. a domain). |
| title | The reduction theorem for algebras of one-sided subshifts over arbitrary alphabets |
| topic | Rings and Algebras Dynamical Systems Operator Algebras 6S10, 16S88, 16N20, 16N60 |
| url | https://arxiv.org/abs/2306.14983 |