Cyclic elements in semisimple lie algebras

Cyclic elements in semisimple lie algebras

We develop a theory of cyclic elements in semisimple Lie algebras. This notion was introduced by Kostant, who associated a cyclic element with the principal nilpotent and proved that it is regular semisimple. In particular, we classfiy all nilpotents giving rise to semisimple and regular semisimple...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Transformation groups 2013-03, Vol.18 (1), p.97-130
Hauptverfasser: Elashvili, A. G., Kac, V. G., Vinberg, E. B.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We develop a theory of cyclic elements in semisimple Lie algebras. This notion was introduced by Kostant, who associated a cyclic element with the principal nilpotent and proved that it is regular semisimple. In particular, we classfiy all nilpotents giving rise to semisimple and regular semisimple cyclic elements. As an application, we obtain an explicit construction of all regular elements in Weyl groups.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-013-9214-0