On the composition of quadratic forms

On the Composition of Quadratic Forms.

The fundamental problem of this theory is to determine a compound of two given forms and the transformation under which the relationship exists. This problem has been considered f by Gauss, Arndt, Dedekind and others. The method of DedekindJ was based upon a correspondence between forms and moduls in an algebraic field, composition of forms corresponding to multiplication of moduls. The method ...

A Generalized Composition of Quadratic Forms based on Quadratic Pairs

For quadratic spaces which represent 1 there is a characterization of hermitian compositions in the language of algebras-with-involutions using the even Clifford algebra. We extend this notion to define a generalized composition based on quadratic pairs and determine the degrees of minimal compositions for any given quadratic pair.

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Composition of Binary Quadratic Forms

Infinite-dimensional Quadratic Forms Admitting Composition

In [2] Albert proved that a finite-dimensional absolute-valued algebra over the reals is necessarily alternative (and hence the reals, complexes, quaternions, or Cayley numbers). In [3] he extended this from finite-dimensional to algebraic algebras. Recently, Wright [9] succeeded in removing the assumption that the algebra is algebraic. Wright proceeds by proving that the norm springs from an i...