Classification of nilpotent elements in simple exceptional real Lie algebras of inner type and description of their centralizers
The nilpotent orbits of a connected Lie group \(G_ 0\) in its Lie algebra \({\mathfrak g}_ 0\) which is supposed to be a simple exceptional non-compact real Lie algebra of inner type are classified. By this a conjecture of Kostant is used which has been recently proved by \textit{J. Sekiguchi} (information supplied by D. R. King in a letter to the author) [J. Math. Soc. Japan 39, 127-138 (1987; Zbl 0627.22008)] and by the author [Trans. Am. Math. Soc. 302, 577-585 (1987; Zbl 0631.17004)] independently. For each nilpotent element \(E\in {\mathfrak g}_ 0\), \(E\neq 0\) (i.e. such that ad E is nilpotent), the dimension of the orbit and the Levi factor of the centralizer of E in \({\mathfrak g}_ 0\) are determined. The results are shown in fifteen tables. Some results of A. V. Alekseevskij, E. B. Dynkin, E. B. Vinberg, A. G. Elashvili are used.
simple exceptional non-compact real Lie algebra of inner type
scientific article; zbMATH DE number 4042120
scientific article