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 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.