On tensorial absorption of the Jiang-Su algebra

Johanesova, Miroslava (2016) On tensorial absorption of the Jiang-Su algebra. PhD thesis, University of Nottingham.

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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.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Winter, Wilhelm
Pumpluen, Susanne
Keywords: C*-algebras, Jiang-Su algebra, Z-stability
Subjects: Q Science > QA Mathematics > QA150 Algebra
Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 33306
Depositing User: Johanesova, Miroslava
Date Deposited: 21 Jul 2016 06:40
Last Modified: 01 Jan 2018 21:39
URI: https://eprints.nottingham.ac.uk/id/eprint/33306

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