JournalsrmiVol. 31, No. 1pp. 245–266

Fine gradings and gradings by root systems on simple Lie algebras

  • Alberto Elduque

    Universidad de Zaragoza, Spain
Fine gradings and gradings by root systems on simple Lie algebras cover
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Abstract

Given a fine abelian group grading Γ ⁣:L=gGLg\Gamma\,\colon\, \mathcal L=\bigoplus_{g\in G}\mathcal L_g on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with GG being the universal grading group, it is shown that the induced grading by the free group G/tor(G)G/\mathrm {tor}(G) on L\mathcal L is a grading by a (not necessarily reduced) root system.

Some consequences for the classification of fine gradings on the exceptional simple Lie algebras are deduced.

Cite this article

Alberto Elduque, Fine gradings and gradings by root systems on simple Lie algebras. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 245–266

DOI 10.4171/RMI/832