Self-similar group actions and KMS states

Mike Whittaker (University of Glasgow)

Tuesday 1st December, 2015 16:00-17:00 Maths 522


A self-similar action (G,X) consists of a group G along with a self-similar action of the group on a rooted tree. Self-similarity is displayed by the action of the group acting on all levels of the tree, in a similar fashion to fractals where patterns are repeated at all scales. Self-similar actions give rise to Cuntz-Pimsner algebras, first constructed by Nekrashevych, as well as a universal Toeplitz algebra. We describe KMS states on these algebras and how they give rise to a new trace on the group algebra. This was joint work with Marcelo Laca, Iain Raeburn, and Jacqui Ramagge.

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