Shift-tail equivalence and an unbounded representative of the Cuntz-Pimsner extension

Authors

Magnus Goffeng, Chalmers University of Technology,
Bram Mesland, Leibniz University of Hannover
Adam C. Rennie, University of WollongongFollow

RIS ID

121423

Publication Details

Goffeng, M., Mesland, B. & Rennie, A. (2018). Shift-tail equivalence and an unbounded representative of the Cuntz-Pimsner extension. Ergodic Theory and Dynamical Systems, 38 (4), 1389-1421.

Abstract

We show how the fine structure in shift-tail equivalence, appearing in the non-commutative geometry of Cuntz-Krieger algebras developed by the first two listed authors, has an analogue in a wide range of other Cuntz-Pimsner algebras. To illustrate this structure, and where it appears, we produce an unbounded representative of the defining extension of the Cuntz-Pimsner algebra constructed from a finitely generated projective bi-Hilbertian module, extending work by the third listed author with Robertson and Sims. As an application, our construction yields new spectral triples for Cuntz and Cuntz-Krieger algebras and for Cuntz-Pimsner algebras associated to vector bundles twisted by an equicontinuous -automorphism.

Grant Number

ARC/DP120100507