The factor type of dissipative KMS weights on graph C*-algebras

TL;DR

This paper computes the Connes S-invariant for von Neumann algebra factors derived from KMS-weights on simple graph C*-algebras, specifically when the measure is dissipative under the shift, advancing understanding of their factor types.

Contribution

It provides a calculation of the S-invariant for factors associated with dissipative measures on graph C*-algebras, a novel contribution to the classification of these factors.

Findings

Determined the S-invariant for dissipative KMS-weights

Classified the factor types arising from these weights

Extended the analysis to generalized gauge actions on graph C*-algebras

Abstract

We calculate the S-invariant of Connes for the von Neumann algebra factors arising from KMS-weights of a generalized gauge action on a simple graph C*-algebra when the associated measure on the infinite path space of the graph is dissipative under the action of the shift.