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BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS

Part of: Selfadjoint operator algebras Ergodic theory

Published online by Cambridge University Press:  12 March 2018

DANIEL GONÇALVES ,
HUI LI  and
DANILO ROYER
DANIEL GONÇALVES
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil e-mail: [email protected]
HUI LI
Affiliation:
Research Center for Operator Algebras and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics, East China Normal University, 3663 Zhongshan North Road, Putuo District, Shanghai 200062, China e-mail: [email protected]
DANILO ROYER
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil e-mail: [email protected]
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Abstract

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We define branching systems for finitely aligned higher-rank graphs. From these, we construct concrete representations of higher-rank graph C*-algebras on Hilbert spaces. We prove a generalized Cuntz–Krieger uniqueness theorem for periodic single-vertex 2-graphs. We use this result to give a sufficient condition under which representations of periodic single-vertex 2-graph C*-algebras arising from branching systems are faithful.

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 37A55: Relations with the theory of $C^*$-algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 731 - 751
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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