On tensorial absorption of the Jiang-Su algebra
The Jiang-Su algebra Z and the notion of Z-stability (i.e. tensorial absorption of the Jiang-Su algebra) are now widely acknowledged to be of particular importance in the classification and structure theory of separable nuclear C*-algebras. The key results in this thesis are early attempts to explor...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2016
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| Online Access: | https://eprints.nottingham.ac.uk/33306/ |
| _version_ | 1848794601711730688 |
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| author | Johanesova, Miroslava |
| author_facet | Johanesova, Miroslava |
| author_sort | Johanesova, Miroslava |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The Jiang-Su algebra Z and the notion of Z-stability (i.e. tensorial absorption of the Jiang-Su algebra) are now widely acknowledged to be of particular importance in the classification and structure theory of separable nuclear C*-algebras. The key results in this thesis are early attempts to explore Z-stability outside the constraints of unital and of nuclear C*-algebras.
Standard unitisations of a separable Z-stable C*-algebra are not Z-stable and we therefore explore possible unitisations that preserve Z-stability. We construct the minimal Z-stable unitisation of a separable Z-stable C*-algebra and show that it satisfies an appropriate universal property.
An interesting area in which to exploit Z-stability outside of the context of nuclear C*-algebras is the so-called Kadison’s similarity problem. We show that the tensor product of two separable unital C*-algebras has Kadison’s similarity property if one of them is nuclear and admits a unital *-homomorphism from (the building blocks of) the Jiang-Su algebra. An immediate consequence of this is that any separable unital Z-stable C*-algebra also has this property. |
| first_indexed | 2025-11-14T19:18:47Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-33306 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:18:47Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-333062025-02-28T13:27:13Z https://eprints.nottingham.ac.uk/33306/ On tensorial absorption of the Jiang-Su algebra Johanesova, Miroslava The Jiang-Su algebra Z and the notion of Z-stability (i.e. tensorial absorption of the Jiang-Su algebra) are now widely acknowledged to be of particular importance in the classification and structure theory of separable nuclear C*-algebras. The key results in this thesis are early attempts to explore Z-stability outside the constraints of unital and of nuclear C*-algebras. Standard unitisations of a separable Z-stable C*-algebra are not Z-stable and we therefore explore possible unitisations that preserve Z-stability. We construct the minimal Z-stable unitisation of a separable Z-stable C*-algebra and show that it satisfies an appropriate universal property. An interesting area in which to exploit Z-stability outside of the context of nuclear C*-algebras is the so-called Kadison’s similarity problem. We show that the tensor product of two separable unital C*-algebras has Kadison’s similarity property if one of them is nuclear and admits a unital *-homomorphism from (the building blocks of) the Jiang-Su algebra. An immediate consequence of this is that any separable unital Z-stable C*-algebra also has this property. 2016-07-21 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/33306/1/Miroslava%20Johanesova%20On%20Tensorial%20Absorption%20of%20the%20Jiang-Su%20Algebra%202016.pdf Johanesova, Miroslava (2016) On tensorial absorption of the Jiang-Su algebra. PhD thesis, University of Nottingham. C*-algebras Jiang-Su algebra Z-stability |
| spellingShingle | C*-algebras Jiang-Su algebra Z-stability Johanesova, Miroslava On tensorial absorption of the Jiang-Su algebra |
| title | On tensorial absorption of the Jiang-Su algebra |
| title_full | On tensorial absorption of the Jiang-Su algebra |
| title_fullStr | On tensorial absorption of the Jiang-Su algebra |
| title_full_unstemmed | On tensorial absorption of the Jiang-Su algebra |
| title_short | On tensorial absorption of the Jiang-Su algebra |
| title_sort | on tensorial absorption of the jiang-su algebra |
| topic | C*-algebras Jiang-Su algebra Z-stability |
| url | https://eprints.nottingham.ac.uk/33306/ |