Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras
classification
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keywords
algebraspreliealgebracomplexenvelopingidealsleftsimple
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We characterize prelie algebras in words of left ideals of the enveloping algebras and in words of modules, and use this result to prove that a simple complex finite-dimensional Lie algebra is not prelie, with the possible exception of f4.
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