Generators of simple Lie algebras in arbitrary characteristics |
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Authors: | Jean-Marie Bois |
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Institution: | (1) Department of Mathematics, University of Bielefeld, P.O. Box 10 01 31, 33501 Bielefeld, Germany |
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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.
The author was partially supported by the European Community’s Human Potential Programme under contract HPRN-CT-2002-00287
(RTN Network “K-Theory, Algebraic Groups and Related Structures”) and a long-term research grant from the D.A.A.D. |
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