Equivariant $\mathcal{D}$-stability for Actions of Tensor Categories
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910814980538368 |
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| author | Evington, Samuel Pacheco, Sergio Girón Jones, Corey |
| author_facet | Evington, Samuel Pacheco, Sergio Girón Jones, Corey |
| contents | We introduce a notion of equivariant $\mathcal{D}$-stability for actions of unitary tensor categories on C$^*$-algebras. We show that, when $\mathcal{D}$ is strongly self-absorbing, equivariant $\mathcal{D}$-stability of an action is equivalent to a unital embedding of $\mathcal{D}$ into a certain subalgebra of Kirchberg's central sequence algebra. We use this to show $\mathcal{Z}$-stability for a large class of AF-actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant $\mathcal{D}$-stability for Actions of Tensor Categories Evington, Samuel Pacheco, Sergio Girón Jones, Corey Operator Algebras Quantum Algebra 46L35, 46L37, 46L55, 18D10 We introduce a notion of equivariant $\mathcal{D}$-stability for actions of unitary tensor categories on C$^*$-algebras. We show that, when $\mathcal{D}$ is strongly self-absorbing, equivariant $\mathcal{D}$-stability of an action is equivalent to a unital embedding of $\mathcal{D}$ into a certain subalgebra of Kirchberg's central sequence algebra. We use this to show $\mathcal{Z}$-stability for a large class of AF-actions. |
| title | Equivariant $\mathcal{D}$-stability for Actions of Tensor Categories |
| topic | Operator Algebras Quantum Algebra 46L35, 46L37, 46L55, 18D10 |
| url | https://arxiv.org/abs/2401.14238 |