Đoković, Dragomir Ž. Classification of nilpotent elements in simple exceptional real Lie algebras of inner type and description of their centralizers. (English) Zbl 0639.17005 J. Algebra 112, No. 2, 503-524 (1988). 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 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. Reviewer: G.I.Zhitomirskij Cited in 3 ReviewsCited in 30 Documents MSC: 17B20 Simple, semisimple, reductive (super)algebras 22E15 General properties and structure of real Lie groups 22E60 Lie algebras of Lie groups Keywords:nilpotent orbits; connected Lie group; simple exceptional non-compact real Lie algebra of inner type; conjecture of Kostant; dimension; Levi factor of the centralizer Citations:Zbl 0627.22008; Zbl 0631.17004 PDFBibTeX XMLCite \textit{D. Ž. Đoković}, J. Algebra 112, No. 2, 503--524 (1988; Zbl 0639.17005) Full Text: DOI References: [1] Alekseevskii, A. V., Component groups of centralizer for nilpotent elements in semisimple algebraic groups, Trudy Tbiliss. Mat. Inst. Razmadze Acad. Nauk Gruzin. SSR, 62, 5-27 (1979), [Russian] · Zbl 0455.20033 [2] Antonyan, L. V., Classification of four-vectors of the eight-dimensional space, (Trudy Semin. Vektor. Tenzor. Aanl., 20 (1981)), 144-161 · Zbl 0467.15018 [3] Bourbaki, N., Groupes et Algèbres de Lie (1968), Hermann: Hermann Paris, Chapitres IV, V et VI · Zbl 0186.33001 [4] Bourbaki, N., Groupes et Algèbres de Lie (1975), Hermann: Hermann Paris, Chapitres VII et VIII · Zbl 0329.17002 [5] \( d̷\) oković, D.Ž., Proof of a conjecture of Kostant, Trans. Amer. Math. Soc., 302, 577-585 (1987) [6] Dynkin, E. B., Amer. Math. Soc. Transl. Ser. 2, 6, 111-245 (1957) · Zbl 0077.03404 [7] Elašvili, A. G., The centralizers of nilpotent elements in semisimple Lie algebras, Trudy Tbiliss. Mat. Inst. Razmadze Acad. Nauk Gruzin. SSR, 46, 109-132 (1975), [Russian] · Zbl 0323.17004 [8] Elkington, G. B., Centralizers of unipotent elements in semisimple algebraic groups, J. Algebra, 23, 137-163 (1972) · Zbl 0247.20053 [10] Kostant, B.; Rallis, S., Orbits and representations associated with symmetric spaces, Amer. J. Math., 93, 753-809 (1971) · Zbl 0224.22013 [12] Vinberg, E. B., Soviet Math. Dokl., 16, 1517-1520 (1975) · Zbl 0374.17001 [13] Vinberg, E. B., Classification of the homogeneous nilpotent elements of a semisimple graded Lie algebra, (Trudy Semin. Vektor. Tenzor. Anal., 19 (1979)), 155-177 · Zbl 0431.17006 [14] Vinberg, E. B.; Elašvili, A. G., Classification of tri-vectors of the 9-dimensional space, (Trudy Semin. Vektor. Tenzor. Anal., 18 (1978)), 197-233 · Zbl 0441.15010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.