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.
Cite
@article{arxiv.1811.11208,
title = {The Magic of Being Exceptional},
author = {Alessio Marrani and Piero Truini and Michael Rios},
journal= {arXiv preprint arXiv:1811.11208},
year = {2019}
}
Comments
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