A ${\mathbb{Z}}_4^3$-grading on a 56-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E

Diego Aranda, Alberto Elduque, Mikhail Kochetov

We describe two constructions of a certain ${\mathbb{Z}}_4^3$-grading on the so-called Brown algebra (a simple structurable algebra of dimension 56 and skew-dimension 1) over an alge…