Geodesic
A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type $E$
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 3, pp. 285-313.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $E_8$.
Classification : 17A30, 17B25, 17B70, 17C40
Keywords: graded algebra; structurable algebra; exceptional simple Lie algebra 
@article{CMUC_2014__55_3_a2,
     author = {Aranda-Orna, Diego and Elduque, Alberto and Kochetov, Mikhail},
     title = {A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple {Lie} algebras of type $E$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {285--313},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2014},
     mrnumber = {3225611},
     zbl = {06391544},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2014__55_3_a2/}
}
TY  - JOUR
AU  - Aranda-Orna, Diego
AU  - Elduque, Alberto
AU  - Kochetov, Mikhail
TI  - A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type $E$
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2014
SP  - 285
EP  - 313
VL  - 55
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2014__55_3_a2/
LA  - en
ID  - CMUC_2014__55_3_a2
ER  - 
%0 Journal Article
%A Aranda-Orna, Diego
%A Elduque, Alberto
%A Kochetov, Mikhail
%T A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type $E$
%J Commentationes Mathematicae Universitatis Carolinae
%D 2014
%P 285-313
%V 55
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2014__55_3_a2/
%G en
%F CMUC_2014__55_3_a2
Aranda-Orna, Diego; Elduque, Alberto; Kochetov, Mikhail. A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type $E$. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 3, pp. 285-313. http://geodesic.mathdoc.fr/item/CMUC_2014__55_3_a2/