Spectral metric spaces on extensions of C*-algebras

Hawkins, A. and Zacharias, J. (2017) Spectral metric spaces on extensions of C*-algebras. Communications in Mathematical Physics, 350(2), pp. 475-506. (doi:10.1007/s00220-016-2820-7)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Zacharias, Dr Joachim
Authors: Hawkins, A., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
Publisher:Springer
ISSN:0010-3616
ISSN (Online):1432-0916
Published Online:01 February 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Communications in Mathematical Physics 350(2):475-4-506
Publisher Policy:Reproduced under a Creative Commons License
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
626331The Cuntz Semigroup and the Fine Stucture of Nuclear C*-AlgebrasJoachim ZachariasEngineering & Physical Sciences Research Council (EPSRC)EP/I019227/2M&S - MATHEMATICS