KMS states on Pimsner algebras associated with C*-dynamical systems

TL;DR

This paper studies KMS states on Pimsner algebras derived from multivariable C*-dynamical systems, revealing that piecewise conjugate classical systems share the same KMS states despite unresolved isomorphism questions.

Contribution

It demonstrates that Pimsner algebras of piecewise conjugate systems have identical KMS states, advancing understanding of their structural properties.

Findings

Pimsner algebras of piecewise conjugate systems share KMS states

KMS states characterize the thermodynamic behavior of these algebras

Open problem remains whether such algebras are *-isomorphic

Abstract

We examine the theory of the KMS states on Pimsner algebras arising from multivariable unital C*-dynamical systems. As an application we show that Pimsner algebras of piecewise conjugate classical systems attain the same KMS states, even though it is still an open problem whether or not they are $*$-isomorphic.