PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

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.

Authors

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image