Fine gradings on ${\mathfrak{e}}_6$

Abstract

There are fourteen fine gradings on the exceptional Lie algebra ${\mathfrak{e}}_6$ over an algebraically closed field of zero characteristic. We provide their descriptions and a proof that they are all.

39 pages

References in corpus (1)

• Group Gradings on Simple Lie Algebras of Type "A"

Cited by in corpus (5)

• Maximal finite abelian subgroups of E8
• Maximal abelian subgroups of compact simple Lie groups of type E
• Fine gradings on the simple Lie algebras of type $E$
• 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
• Weyl groups of the fine gradings on $\e_6$