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arXiv · 1710.09337

KMS and ground states on ultragraph C*-algebras

Gilles Gonçalves de Castro·Daniel Gonçalves
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Abstract

We describe KMS and ground states arising from a generalized gauge action on ultragraph C*-algebras. We focus on ultragraphs that satisfy Condition~(RFUM), so that we can use the partial crossed product description of ultragraph C*-algebras recently described by the second author and Danilo Royer. In particular, for ultragraphs with no sinks, we generalize a recent result by Toke Carlsen and Nadia Larsen: Given a time evolution on the C*-algebra of an ultragraph, induced by a function on the edge set, we characterize the KMS states in five different ways and ground states in four different ways. In both cases we include a characterization given by maps on the set of generalized vertices of the ultragraph. We apply this last result to show the existence of KMS and ground states for the ultragraph C*-algebra that is neither an Exel-Laca nor a graph C*-algebra.

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Gilles Gonçalves de Castro, Daniel Gonçalves. 2017-10-25. KMS and ground states on ultragraph C*-algebras. https://arxiv.org/abs/1710.09337

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