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Riemannian curvature of the noncommutative 3-sphere
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8727-2169
University of Western Ontario, Canada.
2017 (English)In: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 11, no 2, 507-536 p.Article in journal (Refereed) Published
Abstract [en]

In order to investigate to what extent the calculus of classical (pseudo-) Riemannian manifolds can be extended to a noncommutative setting, we introduce pseudo-Riemannian calculi of modules over noncommutative algebras. In this framework, it is possible to prove an analogue of Levi-Civitas theorem, which states that there exists at most one torsion-free and metric connection for a given (metric) module, satisfying the requirements of a real metric calculus. Furthermore, the corresponding curvature operator has the same symmetry properties as the classical Riemannian curvature. As our main motivating example, we consider a pseudo-Riemannian calculus over the noncommutative 3-sphere and explicitly determine the torsion-free and metric connection, as well as the curvature operator together with its scalar curvature.

Place, publisher, year, edition, pages
EUROPEAN MATHEMATICAL SOC , 2017. Vol. 11, no 2, 507-536 p.
Keyword [en]
Noncommutative geometry; 3-sphere; Riemannian curvature; Levi-Civita connection
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-140979DOI: 10.4171/JNCG/11-2-3ISI: 000408582700003OAI: oai:DiVA.org:liu-140979DiVA: diva2:1142302
Note

Funding Agencies|Swedish Research Council

Available from: 2017-09-19 Created: 2017-09-19 Last updated: 2017-09-19

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Arnlind, Joakim
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