C*-algebras of labelled spaces and their diagonal C*-subalgebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Boava, Giuliano¹  de Castro, Gilles G.¹  Mortari, Fernando de L.¹ 

[1] Univ Fed Santa Catarina, Dept Matemat, BR-88040970 Florianopolis, SC, Brazil

关键词: C*-algebra;    Labelled space;    Tight spectrum;   

DOI  :  10.1016/j.jmaa.2017.06.074

来源: Elsevier

【 摘 要 】

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space, inspired by how one might cut or glue labelled paths together, that proves that non-zero elements in the inverse semigroup correspond to non-zero elements in the C*-algebra. We also show that the spectrum of its diagonal C*-subalgebra is homeomorphic to the tight spectrum of the inverse semigroup associated with the labelled space. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free