Approximating rotation algebras and inclusions of C*-algebras

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

Rezvani, Sepideh

关键词: 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;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/97307/REZVANI-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.