Given a fine abelian group grading on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with being the universal grading group, it is shown that the induced grading by the free group on 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. 245–266DOI 10.4171/RMI/832