Generators of simple Lie algebras in arbitrary characteristics

Abstract

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.

26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.3

Cited by in corpus (2)

• Generators of simple Lie algebras II
• On Semi-Modular Subalgebras of Lie Algebras Over Fields of Arbitrary Characteristic