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arXiv · 1512.03455

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

Magnus Goffeng·Bram Mesland·Adam Rennie
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Abstract

We show how the fine structure in shift-tail equivalence, appearing in the noncommutative geometry of Cuntz-Krieger algebras developed by the first two 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 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 equicontinuous $*$-automorphisms.

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BibTeXRIS

Magnus Goffeng, Bram Mesland, Adam Rennie. 2015-12-10. Shift tail equivalence and an unbounded representative of the Cuntz-Pimsner extension. https://doi.org/10.1017/etds.2016.75

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