Cyclic elements in semisimple lie algebras
Author(s)Elashvili, A. G.; Vinberg, E. B.; Kac, Victor
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
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.