De Finetti Theorem on the infinite non-commutative torus
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918122143875072 |
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| author | Crismale, Vitonofrio Del Vecchio, Simone Griseta, Maria Elena Rossi, Stefano |
| author_facet | Crismale, Vitonofrio Del Vecchio, Simone Griseta, Maria Elena Rossi, Stefano |
| contents | The set of spreadabl estates on an infinite non-commutive torus \mathbb{A}_{\mathbb{Z}_α} is determined for all values of the deformation parameter α. If α is irrational, the canonical trace is the only spreadable 2π state. If α is rational, the set of all spreadable states is a Bauer 2π simplex. Moreover, its boundary is the set of all infinite products of a single state on C(T). Finally, the simplex of all stationary states on \mathbb{A}_{\mathbb{Z}_α} is proved to be the Poulsen simplex for all values of the deformation parameter α. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | De Finetti Theorem on the infinite non-commutative torus Crismale, Vitonofrio Del Vecchio, Simone Griseta, Maria Elena Rossi, Stefano Operator Algebras The set of spreadabl estates on an infinite non-commutive torus \mathbb{A}_{\mathbb{Z}_α} is determined for all values of the deformation parameter α. If α is irrational, the canonical trace is the only spreadable 2π state. If α is rational, the set of all spreadable states is a Bauer 2π simplex. Moreover, its boundary is the set of all infinite products of a single state on C(T). Finally, the simplex of all stationary states on \mathbb{A}_{\mathbb{Z}_α} is proved to be the Poulsen simplex for all values of the deformation parameter α. |
| title | De Finetti Theorem on the infinite non-commutative torus |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2508.08044 |