Totally decomposable quadratic pairs

TL;DR

This paper proves that in characteristic two, split central simple algebras with quadratic pairs decomposing into quaternion components are related to quadratic Pfister forms, extending known results to this characteristic.

Contribution

It establishes a new decomposition result for quadratic pairs in characteristic two, linking them to quadratic Pfister forms, which was previously known only in other characteristics.

Findings

Decomposition of quadratic pairs into quaternion components in characteristic two.

Connection between these decompositions and quadratic Pfister forms.

Extension of the Pfister Factor Conjecture to characteristic two.

Abstract

In this paper we show that a split central simple algebra with quadratic pair which decomposes into a tensor product of quaternion algebras with involution and a quaternion algebra with quadratic pair is adjoint to a quadratic Pfister form. This result is new in characteristic two, otherwise it is equivalent to the Pfister Factor Conjecture proven in [3].