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

Abstract

We examine Nica-Pimsner algebras associated with semigroup actions of ${\mathbb{Z}}_{+}^n$ on a C*-algebra $A$ by $\ast$-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.

arXiv comment43 pages; minor corrections; close to publication