Cuntz-Pimsner代数的Cuntz-Krieger唯一性定理
算子代数
2025-02-07 v5
摘要
我们引入C*-对应的一项性质，称之为条件(S)，作为图的条件(L)的类似物。我们利用条件(S)证明Cuntz-Pimsner代数的Cuntz-Krieger唯一性定理，并得到Cuntz-Pimsner代数简单性的充分条件。我们还证明：若Q是无汇点的拓扑箭图且X(Q)为相伴的C*-对应，则X(Q)满足条件(S)当且仅当Q满足条件(L)。最后，我们考察若干例子，以比较并对照条件(S)与Schweizer的非周期条件。
引用
@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}
}
备注
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