J-ternary algebras, structurable algebras, and Lie superalgebras
Rings and Algebras
2026-03-13 v2
Abstract
A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras, specific of this characteristic, are obtained in this way from J-ternary algebras coming from structurable algebras and, in particular, a new magic square of Lie superalgebras is constructed, with entries depending on a pair of composition algebras.
Keywords
Cite
@article{arxiv.2506.18486,
title = {J-ternary algebras, structurable algebras, and Lie superalgebras},
author = {Isabel Cunha and Alberto Elduque},
journal= {arXiv preprint arXiv:2506.18486},
year = {2026}
}
Comments
36 pages