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Intermediate C ^ -algebras of Cartan embeddings
Let A be a C^*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C^*-algebra such that D \subseteq B \subseteq A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, an...
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| Published in: | Proceedings of the American Mathematical Society. Series B 2021-01, Vol.8 (3), p.27-41 |
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| Main Authors: | , , , , |
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| cites | cdi_FETCH-LOGICAL-a2046-716ac5a887ad5d1ef6cd752dbdcc9740b1e3be2826b4e80532dc09fd6624ab143 |
| container_end_page | 41 |
| container_issue | 3 |
| container_start_page | 27 |
| container_title | Proceedings of the American Mathematical Society. Series B |
| container_volume | 8 |
| creator | Brown, Jonathan H. Exel, Ruy Fuller, Adam H. Pitts, David R. Reznikoff, Sarah A. |
| description | Let A be a C^*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C^*-algebra such that D \subseteq B \subseteq A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, and the case when A is nuclear and D is a C^*-diagonal of A. In both cases there is a one-to-one correspondence between the intermediate C^*-algebras B, and a class of open subgroupoids of the groupoid G, where \Sigma \rightarrow G is the twist associated with the embedding D \subseteq A. |
| doi_str_mv | 10.1090/bproc/66 |
| format | article |
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| ispartof | Proceedings of the American Mathematical Society. Series B, 2021-01, Vol.8 (3), p.27-41 |
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| language | eng |
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| subjects | Research article |
| title | Intermediate C ^ -algebras of Cartan embeddings |
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