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BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS

Published online by Cambridge University Press:  12 March 2018

DANIEL GONÇALVES
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil e-mail: daemig@gmail.com
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: lihui8605@hotmail.com
DANILO ROYER
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil e-mail: danilo.royer@ufsc.br
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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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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