Z-stable graph algebras

11.12.2025, 15:00  –  2.09.0.17 (and over Zoom)
Forschungsseminar: Gruppen und Operatoralgebren

Gregory Faurot (Ohio State University)

Abstract: Z-stability is an important regularity property necessary to classify simple C*-algebras. In the case of simple C*-algebras, Z-stability is known to be equivalent to finite nuclear dimension, a noncommutative analogue of covering dimension. Seeking to extend this result beyond the simple case, we examine Z-stability of graph C*-algebras, a well-understood class of C*-algebras due to the close relationship between a graph algebra and its underlying graph. Condition (K) is a particularly important graphical property, as it is known to be necessary for the graph algebra to be Z-stable. In this talk, we introduce another necessary graphical condition for Z-stability that is sufficient (with Condition (K)) when the graph algebra either has finitely many ideals or is AF.