KMS and Ground States on Ultragraph C*-Algebras
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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.
KeywordsKMS states Ultragraph C*-algebras Partial crossed product
Mathematics Subject ClassificationPrimary 46L30 Secondary 46L55
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.
- 2.Afsar, Z., Sims, A.: KMS states on the \(C^*\)-algebras of fell bundles over groupoids (2017). arXiv:1708.00629
- 14.Gonçalves, D., Sobottka, M.: Continuous shift commuting maps between ultragraph shift spaces. Discrete Contin. Dyn. Syst. (2018, to appear). arXiv:1802.04793 [math.DS]
- 15.Imanfar, M., Pourabbas, A., Larki, H.: The Leavitt path algebras of ultragraphs (2017). arXiv:1701.00323
- 21.Raeburn, I.: Graph Algebras, volume 103 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC. American Mathematical Society, Providence (2005)Google Scholar