Symmetries on the real form ${\mathfrak{e}}_{6,-26}$

Abstract

We describe four fine gradings on the real form ${\mathfrak{e}}_{6,-26}$. They are precisely the gradings whose complexifications are fine gradings on the complexified algebra ${\mathfrak{e}}_6$. The universal grading groups are ${\mathbb{Z}}_2^6$, $\mathbb{Z}\times {\mathbb{Z}}_2^4$, ${\mathbb{Z}}^2\times {\mathbb{Z}}_2^3$, and ${\mathbb{Z}}_4\times {\mathbb{Z}}_2^4$.

24 pages