Preferred traces on C*-algebras of self-similar groupoids arising as fixed points
Operator Algebras
2018-11-07 v2 Dynamical Systems
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.
Cite
@article{arxiv.1712.00302,
title = {Preferred traces on C*-algebras of self-similar groupoids arising as fixed points},
author = {Joan Claramunt and Aidan Sims},
journal= {arXiv preprint arXiv:1712.00302},
year = {2018}
}
Comments
12 pages; v2: this version matches the published version