# Equilibrium states on Nica-Toeplitz algebras

Zahra Afsar

## Affiliation:

University of Sydney

## Date:

Tue, 14/08/2018 - 12:00pm to 1:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

Given a quasi-lattice ordered group $(G, P)$ and a compactly aligned product system $X$ of essential $C^*$--correspondences over the monoid P, we show that there is a bijection between the gauge-invariant KMS$_\beta$-states on the Nica-Toeplitz algebra $NT (X)$ of $X$ with respect to a gauge-type dynamics, on one side, and the tracial states on the coefficient algebra $A$ 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 $P$ and $X$, and our result can, in principle, be used to study KMS-states at any finite inverse temperature $\beta$.

This is joint work with Nadia Larsen and Sergey Neshveyev.