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 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...

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

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...

Eight-Dimensional Real Quadratic Division Algebras

Given a euclidean vector space V , a linear map η : V ∧ V → V is called dissident in case v, w, η(v∧w) are linearly independent whenever so are v, w ∈ V . The problem of classifying all real quadratic division algebras is reduced to the problem of classifying all eight-dimensional real quadratic division algebras, and further to the problem of classifying all dissident maps η : R ∧ R → R. Shoul...

C*-Algebra numerical range of quadratic elements

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.

Algebras of Degree Eight 265 on Primary Normal Division Algebras