Rational forms of exceptional dual pairs

TL;DR

This paper demonstrates that all exceptional Lie algebras over a number field can be constructed using Tits' method from octonion and cubic Jordan algebras, revealing their rational dual pairs.

Contribution

It identifies rational forms of dual pairs within exceptional Lie algebras derived via Tits' construction, linking algebraic structures over number fields.

Findings

Every exceptional Lie algebra over a number field arises from Tits' construction.

The paper determines rational forms of the dual pairs in these algebras.

It connects derivation algebras of octonions and Jordan algebras to dual pairs.

Abstract

We show that every exceptional Lie algebra over a number field can be obtained by Tits' construction from an octonion algebra O and a cubic Jordan algebra J. In particular, the exceptional Lie algebra contains a dual pair which is the direct sum of the derivation algebras of O and J. We determine rational forms of this dual pair.