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

  title={Preferred traces on C⁎-algebras of self-similar groupoids arising as fixed points},
  author={Joan Claramunt and Aidan Sims},
  journal={Journal of Mathematical Analysis and Applications},
  • J. ClaramuntA. Sims
  • Published 1 December 2017
  • Mathematics
  • Journal of Mathematical Analysis and Applications

C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states.

We introduce the notion of a self-similar action of a groupoid G on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and we show that

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  • Hui LiDilian Yang
  • Mathematics, Computer Science
    International Mathematics Research Notices
  • 2019
The main results generalize the recent work of Exel and Pardo on self-similar graphs and characterize the simplicity of ${{\mathcal{O}}}_{G,\Lambda }$ in terms of the underlying action, and prove that, whenever the action is simple, there is a dichotomy.

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<p>We study the internal structure of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="" alttext="upper C Superscript asterisk"> <mml:semantics>



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