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arXiv · 2212.00248

A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras

Menevşe Eryüzlü·Mark Tomforde
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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.

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Menevşe Eryüzlü, Mark Tomforde. 2022-12-01. A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras. https://arxiv.org/abs/2212.00248

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