STRUCTURAL THEORY OF SPECIAL LIE ALGEBRAS

摘要

The beginnings of the theory of finite-dimensional Lie algebras date back to the end of the XIXth century and are connected with the names of such mathematicians as Sophus Lie, Engel, E. Cartan, Killing, and others. By analogy with group theory, the notions of soluble and nilpotent Lie algebras were introduced. Killing introduced the notions of radicals and semisimple Lie algebras. Later on, the development of the theory of finite-dimensional Lie algebras led to a classification of finite-dimensional simple Lie algebras over a field of zero characteristic, to the proof of the Levi-Mal'cev theorem, and to many other results.