On Nica-Pimsner algebras of C*-dynamical systems over $\mathbb{Z}_+^n$

TL;DR

This paper studies Nica-Pimsner algebras arising from semigroup actions of b actions on a C*-algebra, characterizing their properties and describing KMS states at different temperatures.

Contribution

The paper provides necessary and sufficient conditions for exactness and nuclearity of Nica-Pimsner algebras and parametrizes KMS states using tracial states on the base algebra.

Findings

Conditions for exactness and nuclearity of Nica-Pimsner algebras.

Parametrization of KMS states at finite and zero temperature.

Formula for obtaining tracial states on Nica-Pimsner algebras.

Abstract

We examine Nica-Pimsner algebras associated with semigroup actions of $\mathbb{Z}_+^n$ on a C*-algebra $A$ by $*$-endomorphisms. We give necessary and sufficient conditions on the dynamics for exactness and nuclearity of the Nica-Pimsner algebras. Furthermore we parameterize the KMS states at finite temperature by the tracial states on $A$. A parametrization is also shown for KMS states at zero temperature (resp. ground states) by the tracial states on $A$ (resp. states on $A$). Finally we give a formula for obtaining tracial states on the Nica-Pimsner algebras.