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.

中文翻译：

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李半代数中的半循环元素

本文是由Elashvili，Kac和Vinberg开发的半简单李代数中循环元素理论的延续。其主要结果是对半简单李代数中的半简单循环元素进行分类。这种分类的重要性源于以下事实：每个这样的元素都会产生Drinfeld–Sokolov型哈密顿量PDE的可积分层次。