2 8 Se p 20 09 The Degree of an Eight - Dimensional Real Quadratic Division Algebra is 1 , 3 , or 5 Ernst Dieterich and Ryszard Rubinsztein
نویسنده
چکیده
A celebrated theorem of Hopf, Bott, Milnor, and Kervaire [11],[1],[12] 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 [6],[3],[9], 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. It was conjectured in [7]. Mathematics Subject Classification 2000: 17A35, 17A45, 55P91.
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The Degree of an Eight - Dimensional Real Quadratic Division Algebra is 1 , 3 , or 5 Ernst Dieterich and Ryszard Rubinsztein
A celebrated theorem of Hopf, Bott, Milnor, and Kervaire [11],[1],[12] 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 [6],[3],[9], the problem of classifying all 8-dimensional real quadratic division algebras is still open. We...
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