Approximating rotation algebras and inclusions of C*-algebras

Rezvani, Sepideh

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https://hdl.handle.net/2142/97307 Copy

Description

Title

Approximating rotation algebras and inclusions of C*-algebras

Author(s)

Rezvani, Sepideh

Issue Date

2017-04-06

Director of Research (if dissertation) or Advisor (if thesis)

Junge, Marius

Doctoral Committee Chair(s)

Boca, Florin

Committee Member(s)

• Ruan, Zhong-Jin
• Oikhberg, Timur

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• 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

Abstract

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.

Graduation Semester

2017-05

Type of Resource

text

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

Copyright and License Information

Copyright 2017 Sepideh Rezvani

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