A Cuntz-Krieger uniqueness theorem for Cuntz-Pimsner algebras - Paulovicks, Menevçse Eryüzlü; Tomforde, Mark (MATHEMATICA SCANDINAVICA, 2025)
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.