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Communications in Mathematical Physics

, Volume 350, Issue 2, pp 475–506 | Cite as

Spectral Metric Spaces on Extensions of C*-Algebras

  • Andrew Hawkins
  • Joachim ZachariasEmail author
Open Access
Article
  • 215 Downloads

Abstract

We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect to summability and produces new spectral quantum metric spaces out of given ones. Using our construction we find new spectral triples on the quantum 2- and 3-spheres giving a new perspective on these algebras in noncommutative geometry.

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Kendal CollegeKendalEngland, UK
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowScotland, UK

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