منابع مشابه
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...
متن کاملDoubled quadratic division algebras
The concept of doubling, introduced around 1840 by Hamilton and Graves, associates with any quadratic algebra A over a field k of characterstic not 2 its double V(A) = A×A, with multiplication (w, x)(y, z) = (wy− z̄x, xȳ + zw). It yields an endofunctor on the category of all quadratic k-algebras which is faithful but not full. We study in which respect the division property of a quadratic k-alge...
متن کاملOn Flexible Quadratic Algebras
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
متن کاملQuadratic Division Algebras Revisited ( Remarks On
In his remarkable article “Quadratic division algebras” (Trans. Amer. Math. Soc. 105 (1962), 202–221), J. M. Osborn claims to solve ‘the problem of determining all quadratic division algebras of order 4 over an arbitrary field F of characteristic not two . . . modulo the theory of quadratic forms over F ’ (cf. p. 206). While we shall explain in which respect he has not achieved this goal, we sh...
متن کاملDivision Algebras , Galois Fields , Quadratic Residues
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10113-1