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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the existence of ad-nilpotent elements


Authors: G. M. Benkart and I. M. Isaacs
Journal: Proc. Amer. Math. Soc. 63 (1977), 39-40
MSC: Primary 17B05
MathSciNet review: 0432721
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Abstract: A condition sufficient to guarantee the nilpotence of a derivation of a Lie algebra is given. It is used to obtain an elementary proof that a finite dimensional Lie algebra over an algebraically closed field of arbitrary characteristic necessarily contains an ad-nilpotent element.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0432721-6
PII: S 0002-9939(1977)0432721-6
Keywords: Ad-nilpotent element, modular Lie algebra
Article copyright: © Copyright 1977 American Mathematical Society