A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Eryüzlü, Menevşe, Tomforde, Mark
Format: Preprint
Published: 2022
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917914121076736
author Eryüzlü, Menevşe
Tomforde, Mark
author_facet Eryüzlü, Menevşe
Tomforde, Mark
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2212_00248
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras
Eryüzlü, Menevşe
Tomforde, Mark
Operator Algebras
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.
title A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras
topic Operator Algebras
url https://arxiv.org/abs/2212.00248