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Generators of simple Lie algebras in arbitrary characteristics

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Bielefeld, P.O. Box 10 01 31, 33501, Bielefeld, Germany

    Jean-Marie Bois

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  1. Jean-Marie Bois
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Correspondence to Jean-Marie Bois.

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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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Bois, JM. Generators of simple Lie algebras in arbitrary characteristics. Math. Z. 262, 715–741 (2009). https://doi.org/10.1007/s00209-008-0397-3

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