The degree of an eight-dimensional real quadratic division algebra is 1, 3, or 5

Details The degree of an eight-dimensional real quadratic division algebra is 1, 3, or 5 The degree of an eight-dimensional real quadratic division algebra is 1, 3, or 5

2009-09-28

arxiv.org/abs/0909.5071v1

Mathematics

Rings and Algebras

8 pages

Scientific paper

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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