The Degree of an Eight-Dimensional Real Quadratic Division Algebra is 1, 3, or 5
2010 (English)In: Bulletin des Sciences Mathematiques, ISSN 0007-4497, Vol. 134, no 5, 447-453 p.Article in journal (Refereed) Published
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.
Real quadratic division algebra, degree, real projective space, fundamental group, liftings.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-108741DOI: 10.1016/j.bulsci.2009.10.001ISI: 000280613700001OAI: oai:DiVA.org:uu-108741DiVA: diva2:240597