Equilibrium states on Nica-Toeplitz algebras

Abstract:

Given a quasi-lattice ordered group (G,P)(G,P) and a compactly aligned product system XX of essential C∗C∗--correspondences over the monoid P, we show that there is a bijection between the gauge-invariant KMSββ-states on the Nica-Toeplitz algebra NT(X)NT(X) of XX with respect to a gauge-type dynamics, on one side, and the tracial states on the coefficient algebra AA satisfying a system (in general infinite) of inequalities, on the other. This strengthens and generalizes a number of results in the literature in several directions: we do not make any extra assumptions on PP and XX, and our result can, in principle, be used to study KMS-states at any finite inverse temperature ββ.

This is joint work with Nadia Larsen and Sergey Neshveyev.