Primitive ideal space of higher-rank graph C*-algebras and decomposability

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Larki, Hossein¹ 

[1] Shahid Chamran Univ Ahvaz, Dept Math, Ahvaz, Iran

关键词: k-Graph;    Higher-rank graph C*-algebra;    Primitive ideal;    Decomposability;   

DOI  :  10.1016/j.jmaa.2018.08.049

来源: Elsevier

【 摘 要 】

In this paper, we describe primitive ideal space of the C*-algebra C* (Lambda) associated to any locally convex row-finite k-graph Lambda. To do this, we will apply the Farthing's desourcifying method on a recent result of Carlsen, Kang, Shotwell, and Sims. We also characterize certain maximal ideals of C* (Lambda). Furthermore, we study the decomposability of C* (Lambda). We apply the description of primitive ideals to show that if I is a direct summand of C*(Lambda), then it is gauge-invariant and isomorphic to a certain k-graph C*-algebra. So, we may characterize decomposable higher-rank C*-algebras by giving necessary and sufficient conditions for the underlying k-graphs. Moreover, we determine all such C*-algebras which can be decomposed into a direct sum of finitely many indecomposable C*-algebras. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free