Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations

Abstract

A representation of the exceptional Lie algebras is presented. It reflects a simple unifying view and it is realized in terms of Zorn-type matrices. The role of the underlying Jordan pair and Jordan algebra content is crucial in the development of the structure. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. Applications in physics are outlined.

arXiv comment1+33 pages; 4 Figures, 2 Tables. v2 : some References added

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Cited by in corpus (13)

• Gravity as the square of Yang-Mills?
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• An octonionic construction of $E_8$ and the Lie algebra magic square
• The Geometry of Exceptional Super Yang-Mills Theories
• The Magic of Being Exceptional
• Vertex operators for an expanding universe
• Sextonions, Zorn Matrices, and ${\mathbf{e}}_{7\frac{1}{2}}$
• A New Division Algebra Representation of $E_7$
• Exceptional Periodicity and Magic Star Algebras. II : Gradings and HT-Algebras
• Exceptional Periodicity and Magic Star Algebras. I : Foundations
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• A New Division Algebra Representation of $E_6$
• Vinberg's T-Algebras. From Exceptional Periodicity to Black Hole Entropy