On the generators of semisimple lie algebras

AbstractIt will be shown that given any element X in a simple Lie algebra Q over C, there exists a Y ∈ Q such that the Lie algebra generated by X and Y is Q. The result is extended to the real semisimple Lie algebras. In some sense the main theorem of this paper can be regarded as an extension of Morozov-Jacobson theorem concerning three dimensional simple Lie algebras (see the remark at the end of Sec. 4). A new property of a special class of regular elements, known as the cyclic elements, is given