Applications of quadratic D-forms to generalized quadratic forms

Abstract

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.

Keywords

• quadratic form
• generalized quadratic form
• division algebra with involution
• right vector space.