Gradings on the simple real Lie algebras of types $G_2$ and $D_4$

Abstract

We classify group gradings on the simple Lie algebras of types $G_2$ and $D_4$ over the field of real numbers (or any real closed field): fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism.

arXiv comment38 pages

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• Gradings on the Lie algebra $D_4$ revisited
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Cited by in corpus (6)

• Gradings on associative algebras with involution and real forms of classical simple Lie algebras
• Graded Lie-Rinehart algebras
• Fine gradings and automorphism groups on associative algebras
• Gradings on the real form ${\mathfrak{e}}_{6,-14}$
• On nonassociative graded-simple algebras over the field of real numbers
• Gradings on simple real Lie algebras