# The canonical quadratic pair on a Clifford algebra and triality

## TL;DR

This paper introduces a canonical quadratic pair on Clifford algebras, extending triality concepts to characteristic 2 and characterizing totally decomposable quadratic pairs in degree 8, with applications to algebras of small Schur index.

## Contribution

It defines a canonical quadratic pair on Clifford algebras and extends triality notions to characteristic 2, providing new characterizations of quadratic pairs.

## Key findings

- Extended trialitarian triples to characteristic 2
- Characterized totally decomposable quadratic pairs in degree 8
- Described trialitarian triples involving small Schur index algebras

## Abstract

We define a canonical quadratic pair on the Clifford algebra of an algebra with quadratic pair over a field. This allows us to extend to the characteristic 2 case the notion of trialitarian triples, from which we derive a characterization of totally decomposable quadratic pairs in degree 8. We also describe trialitarian triples involving algebras of small Schur index.