On Lie gradings. III: Gradings of the real forms of classical Lie algebras (Q1580525)

The authors classify maximal Abelian subgroups of diagonalizable automorphisms (in short MAD-groups) of the real forms of the classical Lie algebras. In part II [ibid. 277, 97-125 (1998; Zbl 0939.17020)] the same was done in the complex case. MAD-groups can be used to produce fine gradings of the Lie algebra. For a simple complex Lie algebra you get all fine gradings in this way, for the real forms this remains an open question.