An octonionic construction of $E_8$ and the Lie algebra magic square
Group Theory
2023-09-20 v1
Abstract
We give a new construction of the Lie algebra of type , in terms of matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal-Tits magic square of Lie algebras, acting on themselves by commutation.
Keywords
Cite
@article{arxiv.2204.04996,
title = {An octonionic construction of $E_8$ and the Lie algebra magic square},
author = {R. A. Wilson and T. Dray and C. A. Manogue},
journal= {arXiv preprint arXiv:2204.04996},
year = {2023}
}