The Magic of Being Exceptional

Abstract

Starting from the Jordan algebraic interpretation of the "Magic Star" embedding within the exceptional sequence of simple Lie algebras, we exploit the so-called spin factor embedding of rank-3 Jordan algebras and its consequences on the Jordan algebraic Lie symmetries, in order to provide another perspective on the origin of the "Exceptional Periodicity" (EP) and its "Magic Star" structure. We also highlight some properties of the special class of Vinberg's rank-3 (dubbed exceptional) T-algebras, appearing on the tips of the "Magic Star" projection of EP(-generalized, finite-dimensional, exceptional) algebras.

1+8 pages, 2 figures, 3 tables. Presented by AM at the 32nd International Colloquium on Group Theoretical Methods in Physics, Prague, July 9-13, 2018

References in corpus (2)

• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Classification of simple linearly compact Kantor triple systems over the complex numbers

Cited by in corpus (7)

• The Geometry of Exceptional Super Yang-Mills Theories
• Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory
• Warm Dark Matter from Higher-Dimensional Gauge Theories
• Exceptional Periodicity and Magic Star Algebras. I : Foundations
• Exceptional Periodicity and Magic Star Algebras. II : Gradings and HT-Algebras
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras