On the invariants of quadratic differential forms

On “horizontal” Invariants Attached to Quadratic Forms

We introduce series of invariants related to the dimension for quadratic forms over a field, study relationships between them and prove a few results about them. This is the TEX-ing of a manuscript from 1993 entitled Quadratic forms and simple algebras of exponent two. The original manuscript contained an appendix that has appeared in [K3]: I removed it and replaced references to it by referenc...

The Arithmetical Invariants of Quadratic Forms

On rational quadratic differential forms

In linear system theory, we often encounter the situation of investigating some quadratic functionals which represent Lyapunov functions, energy storage, performance measures, e.t.c. Such a quadratic functional is called a quadratic differential form (QDF) in the context of the behavioral approach. In the past works, a QDF is usually defined in terms of a polynomial matrix. The contribution of ...

Clifford Modules and Invariants of Quadratic Forms

We construct new invariants of quadratic forms over commutative rings, using ideas from Topology. More precisely, we de…ne a hermitian analog of the Bott class with target algebraic K-theory, based on the classi…cation of Cli¤ord modules. These invariants of quadratic forms go beyond the classical invariants de…ned via the Cli¤ord algebra. An appendix by J.-P. Serre, of independent interest, de...

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.