Search

A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms. An application of this construction to the Witt index of generalised quadratic forms is also given.

In characteristic two, some criteria are obtained for a symmetric square-central element of a totally decomposable algebra with orthogonal involution, to be contained in an invariant quaternion subalgebra.