The dynamical structure of partial group algebras with relations, with applications to subshift algebras
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914200907939840 |
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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 introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the associated partial group algebra with relations. Under suitable conditions - which always holds if the base ring is a field - we demonstrate that the partial skew group ring can also be described using a topological partial action. Furthermore, we show how subshift algebras can be realized as partial group algebras with relations. Using the topological partial action, we describe simplicity of subshift algebras in terms of the underlying dynamics of the subshift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The dynamical structure of partial group algebras with relations, with applications to subshift algebras Boava, Giuliano de Castro, Gilles G. Gonçalves, Daniel van Wyk, Daniel W. Rings and Algebras Operator Algebras Primary: 16S35. Secondary: 16W22, 37B10, 37B05, 22A22, 46L55 We introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the associated partial group algebra with relations. Under suitable conditions - which always holds if the base ring is a field - we demonstrate that the partial skew group ring can also be described using a topological partial action. Furthermore, we show how subshift algebras can be realized as partial group algebras with relations. Using the topological partial action, we describe simplicity of subshift algebras in terms of the underlying dynamics of the subshift. |
| title | The dynamical structure of partial group algebras with relations, with applications to subshift algebras |
| topic | Rings and Algebras Operator Algebras Primary: 16S35. Secondary: 16W22, 37B10, 37B05, 22A22, 46L55 |
| url | https://arxiv.org/abs/2412.15951 |