Branching Systems and General Cuntz-Krieger Uniqueness Theorem for Ultragraph C*-algebras
Abstract
We give a notion of branching systems on ultragraphs. From this we build concrete representations of ultragraph C*-algebras on the bounded linear operators of Hilbert spaces. To each branching system of an ultragraph we describe the associated Perron-Frobenius operator in terms of the induced representation. We show that every permutative representation of an ultragraph C*-algebra is unitary equivalent to a representation arising from a branching system. We give a sufficient condition on ultragraphs such that a large class of representations of the C*-algebras of these ultragraphs is permutative. To give a sufficient condition on branching systems so that their induced representations are faithful we generalize Szyma{\'n}ski's version of the Cuntz-Krieger uniqueness theorem for ultragraph C*-algebras.
Keywords
Cite
@article{arxiv.1601.07005,
title = {Branching Systems and General Cuntz-Krieger Uniqueness Theorem for Ultragraph C*-algebras},
author = {Daniel Gonçalves and Hui Li and Danilo Royer},
journal= {arXiv preprint arXiv:1601.07005},
year = {2016}
}