Rokhlin Dimension: Permanence Properties and Ideal Separation
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929358659125248 |
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| author | M, Sureshkumar Vaidyanathan, Prahlad |
| author_facet | M, Sureshkumar Vaidyanathan, Prahlad |
| contents | We study the Rokhlin dimension for actions of residually finite groups on C*-algebras. We give a definition equivalent to the original one due to Szabo, Wu and Zacharias. We then prove a number of permanence properties and discuss actions on C_0(X)-algebras and commutative C*- algebras. Finally, we use a theorem of Sierakowski to show that, for an action with finite Rokhlin dimension, every ideal in the associated reduced crossed product C*-algebra arises from an invariant ideal of the underlying algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06675 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rokhlin Dimension: Permanence Properties and Ideal Separation M, Sureshkumar Vaidyanathan, Prahlad Operator Algebras Functional Analysis 46L55, 46L40 We study the Rokhlin dimension for actions of residually finite groups on C*-algebras. We give a definition equivalent to the original one due to Szabo, Wu and Zacharias. We then prove a number of permanence properties and discuss actions on C_0(X)-algebras and commutative C*- algebras. Finally, we use a theorem of Sierakowski to show that, for an action with finite Rokhlin dimension, every ideal in the associated reduced crossed product C*-algebra arises from an invariant ideal of the underlying algebra. |
| title | Rokhlin Dimension: Permanence Properties and Ideal Separation |
| topic | Operator Algebras Functional Analysis 46L55, 46L40 |
| url | https://arxiv.org/abs/2305.06675 |