Gradings on the Lie algebra $D_4$ revisited

Abstract

We classify group gradings on the simple Lie algebra $L$ of type $D_4$ over an algebraically closed field of characteristic different from 2: fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism. For each $G$-grading on $L$, we also study graded $L$-modules (assuming characteristic 0).

29 pages

References in corpus (2)

• Graded modules over classical simple Lie algebras with a grading
• Maximal abelian subgroups of compact simple Lie groups of type E

Cited by in corpus (7)

• Gradings on classical central simple real Lie algebras
• Gradings on the simple real Lie algebras of types $G_2$ and $D_4$
• An overview of fine gradings on simple Lie algebras
• Gradings on associative algebras with involution and real forms of classical simple Lie algebras
• Gradings on modules over Lie algebras of E types
• Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras
• Graded simple Lie algebras and graded simple representations