Publication Details

Claramunt, J. & Sims, A. (2018). Preferred traces on C-algebras of self-similar groupoids arising as fixed points. Journal of Mathematical Analysis and Applications, 466 (1), 806-818.


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 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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