Diego Aranda-Orna, Alberto Elduque, Mikhail Kochetov
A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type $E$

Comment.Math.Univ.Carolin. 55,3 (2014) 285-313.

Abstract: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 algebraically closed field of characteristic different from $2$. The Weyl group of this grading is computed. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types $E_6$, $E_7$ and $E_8$.

Keywords: graded algebra; structurable algebra; exceptional simple Lie algebra
AMS Subject Classification: 17B70 17B25 17C40 17A30