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The Degree of an Eight-Dimensional Real Quadratic Division Algebra is 1, 3, or 5
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Algebra and Geometry)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Geometry and Topology)
2010 (English)In: Bulletin des Sciences Mathematiques, ISSN 0007-4497, Vol. 134, no 5, 447-453 p.Article in journal (Refereed) Published
Abstract [en]

A celebrated theorem of Hopf, Bott, Milnor, and Kervaire states that every finite-dimensional real division algebra has dimension 1, 2, 4, or 8. While the real division algebras of dimension 1 or 2 and the real quadratic division algebras of dimension 4 have been classified, the problem of classifying all 8-dimensional real quadratic division algebras is still open. We contribute to a solution of that problem by proving that every 8-dimensional real quadratic division algebra has degree 1, 3, or 5. This statement is sharp.

Place, publisher, year, edition, pages
2010. Vol. 134, no 5, 447-453 p.
Keyword [en]
Real quadratic division algebra, degree, real projective space, fundamental group, liftings.
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-108741DOI: 10.1016/j.bulsci.2009.10.001ISI: 000280613700001OAI: oai:DiVA.org:uu-108741DiVA: diva2:240597
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2012-05-22Bibliographically approved

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Dieterich, Ernst

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