Preferred traces on C*-algebras of self-similar groupoids arising as fixed points

Joan Claramunt; Aidan Sims

doi:10.1016/j.jmaa.2018.06.019

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arXiv · 1712.00302

Preferred traces on C*-algebras of self-similar groupoids arising as fixed points

Joan Claramunt·Aidan Sims

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Abstract

Recent results of Laca, Raeburn, Ramagge and Whittaker show that any self-similar action of a groupoid on a graph determines a 1-parameter family of self-mappings of the trace space of the groupoid C*-algebra. We investigate the fixed points for these self-mappings, under the same hypotheses that Laca et al. used to prove that the C*-algebra of the self-similar action admits a unique KMS state. We prove that for any value of the parameter, the associated self-mapping admits a unique fixed point, which is in fact a universal attractor. This fixed point is precisely the trace that extends to a KMS state on the C*-algebra of the self-similar action.

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BibTeX RIS

Joan Claramunt, Aidan Sims. 2018-11-06. Preferred traces on C*-algebras of self-similar groupoids arising as fixed points. https://doi.org/10.1016/j.jmaa.2018.06.019

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