Pfister involutions in characteristic two

TL;DR

This paper proves that certain central simple algebras with orthogonal involutions in characteristic two are totally decomposable under specific extension conditions, advancing understanding of algebraic structures in characteristic two.

Contribution

It establishes new criteria for total decomposability of algebras with involution in characteristic two, especially relating to anisotropic and metabolic cases, and extends results to quaternion-related algebras.

Findings

Algebras with orthogonal involution are totally decomposable if anisotropic or metabolic over all extensions.

Results apply to algebras Brauer-equivalent to quaternion algebras with Pfister form properties.

Advances understanding of involutions in characteristic two fields.

Abstract

In characteristic two, it is shown that a central simple algebra of degree equal to a power of two with anisotropic orthogonal involution is totally decomposable, if it becomes either anisotropic or metabolic over all extensions of the ground field. A similar result is obtained for the case where this algebra with involution is Brauer-equivalent to a quaternion algebra and it becomes adjoint to a bilinear Pfister form over all splitting fields of the algebra.