# KMS states on Nica-Toeplitz algebras

Sergey Neshveyev (University of Oslo)
Tirsdag 11. september 2018 13:15–14:00 Koll. D (1531-211)
Seminar
Given a quasi-lattice ordered group (G,P) and a compactly aligned product system X of essential C*-correspondences over the monoid P, one defines a C*-algebra NT(X), which is a generalization of a Pimsner-Toeplitz C*-algebra.

We consider a gauge-type dynamics on NT(X) and show that there is a bijection between the gauge-invariant KMS-beta-states on NT(X) and the tracial states on the coefficient algebra A satisfying a system (in general infinite) of inequalities. Under fairly general additional assumptions we show that there is a critical inverse temperature beta_c such that for beta>beta_c all KMS-beta-states are of Gibbs type, in which case we have a complete classification of such states in terms of tracial states on A, while at beta=beta_c we have a phase transition manifesting itself in the appearance of KMS-beta-states that are not of Gibbs type. In the case of right-angled Artin monoids we show also that our system of inequalities for traces on A can be reduced to a much smaller system, a finite one when the monoid is finitely generated. (Joint work with Zahra Afsar and Nadia Larsen.)

Kontakt: Johannes Christensen Revideret: 21.01.2019