Cartan subalgebras in uniform Roe algebras
In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion B⊆A of C∗-algebras is isomorphic to the canonical inclusion of ℓ∞(X) inside a uniform Roe algebra C∗u(X) associated to a metric space of bounded geometry. We o...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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European Mathematical Society
2020
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| _version_ | 1826293021848633344 |
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| author | White, S Willett, R |
| author_facet | White, S Willett, R |
| author_sort | White, S |
| collection | OXFORD |
| description | In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion B⊆A of C∗-algebras is isomorphic to the canonical inclusion of ℓ∞(X) inside a uniform Roe algebra C∗u(X) associated to a metric space of bounded geometry. We obtain uniqueness results for “Roe Cartans” inside uniform Roe algebras up to automorphism when X coarsely embeds into Hilbert space, and up to inner automorphism when X has property A. |
| first_indexed | 2024-03-07T03:23:40Z |
| format | Journal article |
| id | oxford-uuid:b85036f3-5c59-4fca-b0ff-6257c448dbd0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:23:40Z |
| publishDate | 2020 |
| publisher | European Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:b85036f3-5c59-4fca-b0ff-6257c448dbd02022-03-27T04:54:58ZCartan subalgebras in uniform Roe algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b85036f3-5c59-4fca-b0ff-6257c448dbd0EnglishSymplectic Elements at OxfordEuropean Mathematical Society2020White, SWillett, RIn this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion B⊆A of C∗-algebras is isomorphic to the canonical inclusion of ℓ∞(X) inside a uniform Roe algebra C∗u(X) associated to a metric space of bounded geometry. We obtain uniqueness results for “Roe Cartans” inside uniform Roe algebras up to automorphism when X coarsely embeds into Hilbert space, and up to inner automorphism when X has property A. |
| spellingShingle | White, S Willett, R Cartan subalgebras in uniform Roe algebras |
| title | Cartan subalgebras in uniform Roe algebras |
| title_full | Cartan subalgebras in uniform Roe algebras |
| title_fullStr | Cartan subalgebras in uniform Roe algebras |
| title_full_unstemmed | Cartan subalgebras in uniform Roe algebras |
| title_short | Cartan subalgebras in uniform Roe algebras |
| title_sort | cartan subalgebras in uniform roe algebras |
| work_keys_str_mv | AT whites cartansubalgebrasinuniformroealgebras AT willettr cartansubalgebrasinuniformroealgebras |