# Orthogonal involutions and totally singular quadratic forms in characteristic two

## TL;DR

This paper introduces a totally singular quadratic form associated with orthogonal involutions in characteristic two, providing tools for classification and conjugacy criteria of such involutions.

## Contribution

It establishes a new association between quadratic forms and orthogonal involutions in characteristic two, aiding classification and conjugacy analysis.

## Key findings

- Quadratic form reflects anisotropy properties of involution
- Classification of totally decomposable algebras with orthogonal involution
- Criterion for conjugation to transpose involution

## Abstract

We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can be used to classify totally decomposable algebras with orthogonal involution. Also, using this form, a criterion is obtained for an orthogonal involution on a split algebra to be conjugated to the transpose involution.