Faithful Representations of Graph Algebras via Branching Systems

Canadian mathematical bulletin

Daniel Gonçalves¹  Danilo Royer¹  Hui Li² 

[1] Departamento de Matemática - Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brazil;Research Center for Operator Algebras, Department of Mathematics, East China Normal University (Minhang Campus), 500 Dongchuan Road, Minhang District, Shanghai 200241, China

关键词: C*-algebra;    graph algebra;    Leavitt path algebra;    branching system;    representation;   

DOI  :  10.4153/CMB-2015-032-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We continue to investigate branching systems of directed graphs and their connections with graph algebras. We give a sufficient condition under which the representation induced from a branching system of a directed graph is faithful and construct a large class of branching systems that satisfy this condition. We finish the paper by providing a proof of the converse of the Cuntz-Kriegeruniqueness theorem for graph algebras by means of branching systems.

【 授权许可】

Unknown