Gradings on \(\mathfrak {g}_2\)
The authors deal with gradings on simple Lie and Jordan algebras and question ourselves if there are nontoral gradings of simple Lie algebras different from those already known. They develop a method for constructing nontoral gradings refining a toral one when possible and they also give techniques which can be possibly applied in other contexts. They conclude that there are only two fine gradings, one nontoral, 24 toral ones and of these, 20 are equivalent to grading by cyclic groups.
scientific article; zbMATH DE number 5072853