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SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS

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Abstract

This paper is a continuation of the theory of cyclic elements in semisimple Lie algebras, developed by Elashvili, Kac and Vinberg. Its main result is the classification of semisimple cyclic elements in semisimple Lie algebras. The importance of this classification stems from the fact that each such element gives rise to an integrable hierarchy of Hamiltonian PDE of Drinfeld–Sokolov type.

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Authors and Affiliations

  1. Razmadze Mathematical Institute, TSU, 0186, Tbilisi, Georgia

    A. G. ELASHVILI

  2. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    M. JIBLADZE & V. G. KAC

Authors
  1. A. G. ELASHVILI
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  2. M. JIBLADZE
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  3. V. G. KAC
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Correspondence to V. G. KAC.

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M. Jibladze is partially supported by the grant FR-18-10849 of the Shota Rustaveli National Science Foundation of Georgia.

V. G. Kac is partially supported by the Simons Fellowship and by the Bert and Ann Kostant fund.

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ELASHVILI, A.G., JIBLADZE, M. & KAC, V.G. SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS. Transformation Groups 27, 429–470 (2022). https://doi.org/10.1007/s00031-020-09568-2

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