A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras
Abstract
We introduce a property of C*-correspondences, which we call Condition (S), to serve as an analogue of Condition (L) of graphs. We use Condition (S) to prove a Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner algebras and obtain sufficient conditions for simplicity of Cuntz-Pimsner algebras. We also prove that if Q is a topological quiver with no sinks and X(Q) is the associated C*-correspondence, then X(Q) satisfies Condition (S) if and only if Q satisfies Condition(L). Finally, we consider several examples to compare and contrast Condition (S) with Schweizer's nonperiodic condition.
Keywords
Cite
@article{arxiv.2212.00248,
title = {A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras},
author = {Menevşe Eryüzlü and Mark Tomforde},
journal= {arXiv preprint arXiv:2212.00248},
year = {2025}
}
Comments
26 pages, Version II Comments: Title changed to better reflect the main results of the paper. Exposition reworked to provide more motivation and more effectively compare our simplicity result to Schweizer's simplicity theorem. Version IV Comments: Exposition has be improved to include references and comparison to the results of [2]. Version V Comments: Subsection 4.1 and Theorem 4.8 added