Cyclic elements in semisimple lie algebras
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Kac_Cyclic elements.pdf
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277.43 KB
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Author(s)
Elashvili, A. G.
Vinberg, E. B.
Kac, Victor
Date Issued
February 2013
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00031-013-9214-0
