Cyclic elements in semisimple lie algebras

Author(s)
Elashvili, A. G.; Vinberg, E. B.; Kac, Victor
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Abstract
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.
Date issued
2013-02
URI
http://hdl.handle.net/1721.1/92900
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Transformation Groups
Publisher
Springer-Verlag
Citation
Elashvili, A. G., V. G. Kac, and E. B. Vinberg. “Cyclic Elements in Semisimple Lie Algebras.” Transformation Groups 18, no. 1 (February 3, 2013): 97–130.
Version: Original manuscript
ISSN
1083-4362
1531-586X
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