$\mathbb{Z}^{2}$-dimension groups
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914068360593408 |
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| author | Giordano, Thierry Putnam, Ian F. Skau, Christian F. |
| author_facet | Giordano, Thierry Putnam, Ian F. Skau, Christian F. |
| contents | We study a class of simple dimension groups in which the cyclic subgroup generated by the order unit is replaced by a copy of $\mathbb{Z}^{2}$ satisfying some strict conditions. Our main results are necessary and sufficient conditions on a Bratteli diagram which provides inductive limit structures for such groups. This result has an important application in constructing a version of the Bratteli-Vershik model for minimal actions of $\mathbb{Z}^{2}$ on the Cantor set which will be the subject of a subsequent paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{Z}^{2}$-dimension groups Giordano, Thierry Putnam, Ian F. Skau, Christian F. Dynamical Systems 06F20 (Primary)37Bxx (Secondary) We study a class of simple dimension groups in which the cyclic subgroup generated by the order unit is replaced by a copy of $\mathbb{Z}^{2}$ satisfying some strict conditions. Our main results are necessary and sufficient conditions on a Bratteli diagram which provides inductive limit structures for such groups. This result has an important application in constructing a version of the Bratteli-Vershik model for minimal actions of $\mathbb{Z}^{2}$ on the Cantor set which will be the subject of a subsequent paper. |
| title | $\mathbb{Z}^{2}$-dimension groups |
| topic | Dynamical Systems 06F20 (Primary)37Bxx (Secondary) |
| url | https://arxiv.org/abs/2509.26444 |