The flow of weights and the Cuntz-Pimsner algebras

TL;DR

This paper characterizes the flows of weights for von Neumann algebras associated with KMS states on Cuntz-Pimsner algebras using Poisson boundaries, linking operator algebras and probabilistic boundaries.

Contribution

It provides a new description of the flows of weights in terms of Poisson (tail) boundaries for algebras arising from gauge actions.

Findings

Flows of weights are described via Poisson boundaries.

Connects KMS states with probabilistic boundary theory.

Advances understanding of von Neumann algebras from Cuntz-Pimsner structures.

Abstract

We describe the flows of weights for von Neumann algebras arising from KMS states for the gauge actions of the Cuntz-Pimsner algebras in terms of Poisson (tail) boundaries.