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

Diego Aranda-Orna¹ 

关键词: graded algebra;    structurable algebra;    exceptional simple Lie algebra;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 $E_8$.

【 授权许可】

CC BY