Non-abelian gradings of Lie algebras
Volume 113 / 2017
Banach Center Publications 113 (2017), 19-38
MSC: Primary 17B25; Secondary: 17B70, 17C40.
DOI: 10.4064/bc113-0-2
Abstract
We introduce non-abelian gradings of Lie algebras as their isotypic decompositions with respect to reductive groups of automorphisms. The main results relate to a special kind of $\mathrm{SL}_3$-gradings, in terms of which the commutation operation admits a simple description. We show that any simple Lie algebra but $C_n$ admits such a grading, and it is unique up to conjugation.
