On split products of quaternion algebras with involution in characteristic two

TL;DR

This paper proves that in characteristic two, a split tensor product of quaternion algebras with involution can always be expressed as a tensor product of split quaternion algebras with involution, confirming a specific structural property.

Contribution

It establishes an affirmative answer to the question of expressing split tensor products of quaternion algebras with involution as tensor products of split quaternion algebras with involution in characteristic two.

Findings

Split tensor products of quaternion algebras with involution are expressible as tensor products of split quaternion algebras with involution in characteristic two.

The result confirms a structural property of quaternion algebras with involution in characteristic two.

The paper advances understanding of algebraic structures in characteristic two fields.

Abstract

The question of whether a split tensor product of quaternion algebras with involution over a field of characteristic two can be expressed as a tensor product of split quaternion algebras with involution, is shown to have an affirmative answer.