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Title:Approximating rotation algebras and inclusions of C*-algebras
Author(s):Rezvani, Sepideh
Director of Research:Junge, Marius
Doctoral Committee Chair(s):Boca, Florin
Doctoral Committee Member(s):Ruan, Zhong-Jin; Oikhberg, Timur
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Weak expectation property (WEP)
Quotient weak expectation property (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.
Issue Date:2017-04-06
Rights Information:Copyright 2017 Sepideh Rezvani
Date Available in IDEALS:2017-08-10
Date Deposited:2017-05

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