On Regularity of Graph C*-Algebras

Authors

Gregory Joseph Faurot, University of Nebraska-LincolnFollow

First Advisor

Christopher Schafhauser

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

Date of this Version

8-2024

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mathematics

Under the supervision of Professor Christopher Schafhauser

Lincoln, Nebraska, August 2024

Comments

Copyright 2024, Gregory Joseph Faurot. Used by permission

Abstract

We prove that for any countable directed graph E with Condition (K), the corresponding graph C*-algebra C*(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for O_∞ -stability of graph algebras, and prove some partial results for Z-stability.

Advisor: Christopher Schafhauser

Recommended Citation

Faurot, Gregory Joseph, "On Regularity of Graph C*-Algebras" (2024). Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–. 158.
https://digitalcommons.unl.edu/dissunl/158