Classification of nilpotent elements in simple exceptional real Lie algebras of inner type and description of their centralizers
type: Item
instance of: scholarly article
title: Classification of nilpotent elements in simple exceptional real Lie algebras of inner type and description of their centralizers
zbMATH Open document ID: 0639.17005
DOI: 10.1016/0021-8693(88)90104-4
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 4042120
zbMATH Keywords: nilpotent orbits
zbMATH Keywords: connected Lie group
zbMATH Keywords: simple exceptional non-compact real Lie algebra of inner type
zbMATH Keywords: conjecture of Kostant
zbMATH Keywords: dimension
zbMATH Keywords: Levi factor of the centralizer
Wikidata QID: Q115366498
author: Dragomir Ž. Đoković
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90104-4
OpenAlex ID: W2004427275
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description: scientific article; zbMATH DE number 4042120