- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
31
2015
1
Fine gradings and gradings by root systems on simple Lie algebras
Alberto
Elduque
Universidad de Zaragoza, ZARAGOZA, SPAIN
Fine grading, simple Lie algebra, grading by root systems, exceptional, coordinate algebra
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.
Nonassociative rings and algebras
245
266
10.4171/RMI/832
http://www.ems-ph.org/doi/10.4171/RMI/832