On totally decomposable algebras with involution in characteristic two

TL;DR

This paper establishes a criterion for decomposability of central simple algebras with involution in characteristic two and links bilinear Pfister forms to their classification.

Contribution

It provides a necessary and sufficient condition for decomposability and connects bilinear Pfister forms to classifying these algebras in characteristic two.

Findings

Decomposability characterized by Frobenius subalgebras.

Bilinear Pfister forms classify totally decomposable algebras.

Criterion applicable specifically in characteristic two.

Abstract

A necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras with involution, in terms of its Frobenius subalgebras, is given. It is also proved that a bilinear Pfister form, recently introduced by A. Dolphin, can classify totally decomposable central simple algebras of orthogonal type.