The diagonal dimensions for C*-pairs

Kang Li Àî¿µ

*(Friedrich-Alexander-Universitat Erlangen-N¨¹rnberg)*

16:00-17:00, November 21, 2023 Science Building A503 & Tencent Meeting 431576576

__Abstract:__

We will introduce the notion of diagonal dimension for diagonal pairs of C*-algebras in the sense of Kumjian, and will compare it with the usual nuclear dimension for C*-algebras. For instance, the Jiang-Su algebra Z admits a diagonal MASA D such that the diagonal dimension of (Z,D) is equal to n for any given natural number n even though the nuclear dimension of Z is equal to 1. We also show that the diagonal dimension of a uniform Roe algebra with respect to the standard diagonal is equal to the asymptotic dimension of its underlying metric space. Finally, we will discuss its relation to the dynamic asymptotic dimension of groupoids introduced by Guentner, Willett and Yu and the tower dimension of topological dynamical systems introduced by Kerr. This is joint work with Hung-Chang Liao and Wilhelm Winter.

__About the speaker:__

Professor Kang Li received Ph.D. in Mathematics from University of Copenhagen in January 2016 under the supervision of Professor Uffe Haagerup and Professor Ryszard Nest. Currently, he is a Junior Professor for Mathematics in Representation Theory and Operator Algebras at Department of Mathematics of Friedrich-Alexander-Universitat Erlangen-N¨¹rnberg in Germany. Professor Kang Li is affiliated to the Lie Groups leading by Prof. Dr. Karl-Hermann Neeb. His main research area is Operator Algebras and their interactions with Dynamical Systems, Geometric Group Theory and Representation Theory.

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