The Magic Star of Exceptional Periodicity
Abstract
We present a periodic infinite chain of finite generalisations of the exceptional structures, including e8, the exceptional Jordan algebra (and pair), and the octonions. We demonstrate that the exceptional Jordan algebra is part of an infinite family of finite-dimensional matrix algebras (corresponding to a particular class of cubic Vinberg's T-algebras). Correspondingly, we prove that e8 is part of an infinite family of algebras (dubbed "Magic Star" algebras) that resemble lattice vertex algebras.
Keywords
Cite
@article{arxiv.1711.07881,
title = {The Magic Star of Exceptional Periodicity},
author = {Piero Truini and Michael Rios and Alessio Marrani},
journal= {arXiv preprint arXiv:1711.07881},
year = {2025}
}
Comments
1+18 pages, 5 figures; v2 : 1+22 pages, 5 figures; proofs of propositions added, some remarks in Secs. 1 and 7 added, Abstract modified, some typographic changes. Seminar delivered by Michael Rios at the 4th Mile High Conference on Nonassociative Mathematics University of Denver, Denver, Colorado, USA, July 29-August 5, 2017