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arXiv · 1307.0793

A generalized Cuntz-Krieger uniqueness theorem for higher rank graphs

Jonathan H. Brown·Gabriel Nagy·Sarah Reznikoff
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Abstract

We present a uniqueness theorem for k-graph C*-algebras that requires neither an aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity of a representation of a k-graph C*-algebra, it is sufficient that the representation be injective on a distinguished abelian C*-subalgebra. A crucial part of the proof is the application of an abstract uniqueness theorem, which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient C*-algebra, each of which is the unique extension of a state on the distinguished abelian C*-subalgebra.

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Jonathan H. Brown, Gabriel Nagy, Sarah Reznikoff. 2013-07-02. A generalized Cuntz-Krieger uniqueness theorem for higher rank graphs. https://arxiv.org/abs/1307.0793

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