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A NOTE ON DERIVATIONS OF LIE ALGEBRAS

Published online by Cambridge University Press:  21 July 2011

M. SHAHRYARI*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran (email: mshahryari@tabrizu.ac.ir)
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Abstract

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In this note, we will prove that a finite-dimensional Lie algebra L over a field of characteristic zero, admitting an abelian algebra of derivations DDer(L), with the property for some n>1, is necessarily solvable. As a result, we show that if L has a derivation d:LL such that Lnd(L), for some n>1, then L is solvable.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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