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Publication

Isometries of quadratic spaces

Eva Bayer Fluckiger
2015
Journal Articles

Résumé

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the completions of k. This gives a partial answer to a question of Milnor.

Source officielle

Eva Bayer Fluckiger
2015
Journal Articles

Résumé

Source officielle

Concepts associés (23)

Forme quadratique

thumb|L'annulation d'une forme quadratique donne le cône de lumière de la relativité restreinte, son signe fait la différence entre les événements accessibles ou inaccessibles dans l'espace-temps. En mathématiques, une forme quadratique est un polynôme homogène de degré 2 avec un nombre quelconque de variables. Les formes quadratiques d'une, deux et trois variables sont données respectivement par les formules suivantes (a,b,c,d,e,f désignant des coefficients) : L'archétype de forme quadratique est la forme x + y + z sur R, qui définit la structure euclidienne et dont la racine carrée permet de calculer la norme d'un vecteur.

Isotropic quadratic form

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Otherwise the quadratic form is anisotropic. More explicitly, if q is a quadratic form on a vector space V over F, then a non-zero vector v in V is said to be isotropic if q(v) = 0. A quadratic form is isotropic if and only if there exists a non-zero isotropic vector (or null vector) for that quadratic form. Suppose that (V, q) is quadratic space and W is a subspace of V.

Polynôme irréductible

In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the field to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial x2 − 2 is a polynomial with integer coefficients, but, as every integer is also a real number, it is also a polynomial with real coefficients.

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Publications associées (29)

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Isometries of quadratic spaces

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