An octonionic construction of $E_8$ and the Lie algebra magic square
R. A. Wilson, T. Dray, C. A. Manogue
TL;DR
This paper introduces a novel construction of the $E_8$ Lie algebra using $3\times3$ matrices, providing a natural matrix commutator interpretation and offering new insights into the Freudenthal-Tits magic square.
Contribution
It presents a new matrix-based construction of $E_8$ and a reinterpretation of the magic square, enhancing understanding of Lie algebra structures.
Findings
New matrix construction of $E_8$ Lie algebra
Natural description of Lie bracket as matrix commutator
Reinterpretation of the Freudenthal-Tits magic square
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics