Revista Matemática Iberoamericana


Full-Text PDF (301 KB) | Metadata | Table of Contents | RMI summary
Volume 31, Issue 1, 2015, pp. 245–266
DOI: 10.4171/RMI/832

Published online: 2015-03-05

Fine gradings and gradings by root systems on simple Lie algebras

Alberto Elduque[1]

(1) Universidad de Zaragoza, Spain

Given a fine abelian group grading $\Gamma\,\colon\, \mathcal L=\bigoplus_{g\in G}\mathcal L_g$ on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with $G$ being the universal grading group, it is shown that the induced grading by the free group $G/\mathrm {tor}(G)$ on $\mathcal L$ 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.

Keywords: Fine grading, simple Lie algebra, grading by root systems, exceptional, coordinate algebra

Elduque Alberto: Fine gradings and gradings by root systems on simple Lie algebras. Rev. Mat. Iberoamericana 31 (2015), 245-266. doi: 10.4171/RMI/832