Octonionic Planes and Real Forms of G2, F4 and E6
Rings and Algebras
2022-08-09 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
In this work we present a useful way to introduce the octonionic projective and hyperbolic plane through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra and show that the Veronese vectors are the rank-one elements of the algebra. We then study groups of motions over the octonionic plane recovering all real forms of G2, F4and E6 groups and finally give a classification of all octonionic and split-octonionic planes as symmetric spaces.
Keywords
Cite
@article{arxiv.2203.02671,
title = {Octonionic Planes and Real Forms of G2, F4 and E6},
author = {Daniele Corradetti and Alessio Marrani and David Chester and Raymond Aschheim},
journal= {arXiv preprint arXiv:2203.02671},
year = {2022}
}
Comments
16 pages, 3 figures