2022/12/01 by Menevşe Eryüzlü, Eryüzlü, Menevşe, Mark Tomforde +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Quantum Mechanics and Applications #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2212.00248
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.