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

publication date

  • October 2018

start page

  • 806

end page

  • 818


  • 1


  • 466

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813


  • 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.


  • Mathematics


  • c⁎ -algebra; self-similar group; self-similar groupoid; kms state; trace; fixed point