Condition (K) for inverse semigroups and the ideal structure of their C*-algebras

JOURNAL OF ALGEBRA

卷:523

Article

LaLonde, Scott M.¹  Milan, David¹  Scott, Jamie² 

[1] Univ Texas Tyler, Dept Math, 3900 Univ Blvd, Tyler, TX 75799 USA

[2] Univ Florida, Dept Math, 1400 Stadium Rd, Gainesville, FL 32611 USA

关键词: Inverse semigroups;    Groupoids;    Steinberg algebras;    C*-algebras;   

DOI  :  10.1016/j.jalgebra.2018.12.017

来源: Elsevier

【 摘 要 】

Inspired by results for graph C*-algebras, we investigate connections between the ideal structure of an inverse semigroup S and that of its tight C*-algebra by relating ideals in S to certain open invariant sets in the associated tight groupoid. We also develop analogues of Conditions (L) and (K) for inverse semigroups, which are related to certain congruences on S. We finish with applications to the inverse semigroups of self-similar graph actions and some relevant comments on the authors' earlier uniqueness theorems for inverse semigroups. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free