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Non-abelian gradings of Lie algebras

Volume 113 / 2017

Ernest B. Vinberg Banach Center Publications 113 (2017), 19-38 MSC: Primary 17B25; Secondary: 17B70, 17C40. DOI: 10.4064/bc113-0-2


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.


  • Ernest B. VinbergDepartment of Mechanics and Mathematics
    Moscow State University
    Moscow 119991, GSP–1, Russia

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