Some forms of exceptional Lie algebras

TL;DR

This paper constructs certain forms of exceptional Lie algebras (E_6, E_7, E_8) using the exterior cube of a finitely generated projective module of rank 9, providing new algebraic insights.

Contribution

It introduces a novel construction method for some forms of exceptional Lie algebras via exterior algebra of projective modules.

Findings

Constructed new forms of E_6, E_7, E_8 Lie algebras

Demonstrated the use of exterior cube of modules in Lie algebra construction

Provided algebraic framework for understanding exceptional Lie algebras

Abstract

Some forms of Lie algebras of types E_6, E_7, and E_8 are constructed using the exterior cube of a rank 9 finitely generated projective module.