Shift tail equivalence and an unbounded representative of the CuntzPimsner extension
Abstract
We show how the fine structure in shifttail equivalence, appearing in the noncommutative geometry of CuntzKrieger algebras developed by the first two authors, has an analogue in a wide range of other CuntzPimsner algebras. To illustrate this structure, and where it appears, we produce an unbounded representative of the defining extension of the CuntzPimsner algebra constructed from a finitely generated projective biHilbertian module, extending work by the third author with Robertson and Sims. As an application, our construction yields new spectral triples for Cuntz and CuntzKrieger algebras and for CuntzPimsner algebras associated to vector bundles twisted by equicontinuous $*$automorphisms.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.03455
 Bibcode:
 2015arXiv151203455G
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Dynamical Systems;
 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra
 EPrint:
 30 pages