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KMS and Ground States on Ultragraph C*-Algebras

  • Gilles Gonçalves de Castro
  • Daniel Gonçalves
Article
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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 an ultragraph C*-algebra that is neither an Exel–Laca nor a graph C*-algebra.

Keywords

KMS states Ultragraph C*-algebras Partial crossed product 

Mathematics Subject Classification

Primary 46L30 Secondary 46L55 

Notes

Acknowledgements

The authors would like to thank Zahra Afsar for valuable discussions regarding the present paper. In particular, the second author would like to thank Zahra for teaching him the theory of KMS states.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolisBrazil

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