English

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 E8E_8, in terms of 3×33\times3 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}
}
R2 v1 2026-06-24T10:44:17.996Z