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The Degree of an Eight-Dimensional Real Quadratic Division Algebra is 1, 3, or 5PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)In: Bulletin des Sciences Mathematiques, ISSN 0007-4497, Vol. 134, no 5, 447-453 p.Article in journal (Refereed) Published
##### Abstract [en]

##### 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
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2012-05-22Bibliographically approved

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.

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