Approximating rotation algebras and inclusions of C*-algebras

In the first part of this thesis, we will follow Kirchberg’s categorical perspective to establish new notions of WEP and QWEP relative to a C∗-algebra, and develop similar properties as in the classical WEP and QWEP. Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. The focus of the second part of this thesis is the approximation of rotation algebras in the quantum Gromov–Hausdorff distance. We introduce the completely bounded quantum Gromov–Hausdorff distance and show that for even dimensions, the higher dimensional rotation algebras can be approximated by matrix algebras in this sense. Finally, we show that for even dimensions, matrix algebras converge to the rotation algebras in the strongest form of Gromov–Hausdorff distance, namely in the sense of Latrémolière’s Gromov–Hausdorff propinquity.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Rezvani, Sepideh

Contributors dc:contributor

• Junge, Marius
• Boca, Florin
• Ruan, Zhong-Jin
• Oikhberg, Timur

• C*-algebras
• Weak expectation property (WEP)
• Quotient weak expectation property (QWEP)
• A-WEP
• A-QWEP
• Relatively weak injectivity
• Order-unit space
• Noncommutative tori
• Compact quantum metric space
• Conditionally negative length function
• Heat semigroup
• Poisson semigroup
• Rotation algebra
• Continuous field of compact quantum metric spaces
• Gromov–Hausdorff distance
• Completely bounded quantum Gromov–Hausdorff distance
• Gromov–Hausdorff propinquity

Statement dc:rights

• Copyright 2017 Sepideh Rezvani

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/97307

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/97307