Sextonions, Zorn Matrices, and $\mathbf{e_{7 \frac12}}$
Rings and Algebras
2017-05-23 v3 High Energy Physics - Theory
Representation Theory
Abstract
By exploiting suitably constrained Zorn matrices, we present a new construction of the algebra of sextonions (over the algebraically closed field ). This allows for an explicit construction, in terms of Jordan pairs, of the non-semisimple Lie algebra , intermediate between and , as well as of all Lie algebras occurring in the sextonionic row and column of the extended Freudenthal Magic Square.
Cite
@article{arxiv.1506.04604,
title = {Sextonions, Zorn Matrices, and $\mathbf{e_{7 \frac12}}$},
author = {Alessio Marrani and Piero Truini},
journal= {arXiv preprint arXiv:1506.04604},
year = {2017}
}
Comments
version 2 : minor refinements, Eq. (1.2) removed, and App. A added, in which we prove that - on R - the split sextonions do not contain the divisional quaternions. 14 pages, 6 figures. version 3 : Refs. added, various refinements; matches published version on Lett. Math. Phys