The bracket of the exceptional Lie algebra E8
Differential Geometry
2026-05-19 v3 Group Theory
Rings and Algebras
Abstract
We obtain an explicit formula for the bracket of the exceptional simple Lie algebra E8 based on triality and oct-octonions, following the Barton-Sudbery description of E8. Furthermore, we provide descriptions of the subalgebras E6 and E7 and prove an explicit formula for the 26-dimensional irreducible representation of F4.
Keywords
Cite
@article{arxiv.2504.16513,
title = {The bracket of the exceptional Lie algebra E8},
author = {Andreas Kollross},
journal= {arXiv preprint arXiv:2504.16513},
year = {2026}
}
Comments
13 pages; v2: expanded introduction; v3: a description of the subalgebras E6 and E7 was included, an explicit formula for the 26-dimensional irreducible representation of F4 is provided, updated references, other minor corrections, 17 pages;