The bracket of the exceptional Lie algebra E8

2025/04/23 by Andreas Kollross, Kollross, Andreas
Mathematics · #17B25 (Primary) 17A35 #22E60 #53C35 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2504.16513

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

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.

Citations

• On Separation of Variables for Symmetric Spaces of Rank1
• Octonions, triality, the exceptional Lie algebra F4, and polar actions on the Cayley hyperbolic plane
• 𝐸₈, the most exceptional group
• Invariant four-forms and symmetric pairs
• Tits construction of the exceptional simple Lie algebras
• A geometric construction of the exceptional Lie algebras F4 and E8
• Magic squares and matrix models of Lie algebras
• The Octonions
• The octonions
• The greatest mathematical paper of all time
• Die Zusammensetzung der stetigen endlichen Transformationsgruppen
• Differential Geometry, Lie Groups, and Symmetric Spaces

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