Lie elements in pre-Lie algebras, trees and cohomology operations

Abstract

We give a simple characterization of Lie elements in free pre-Lie algebras as elements of the kernel of a map between spaces of trees. We explain how this result is related to natural operations on the Chevalley-Eilenberg complex of a Lie algebra. We also indicate a possible relation to Loday's theory of triplettes.

arXiv comment21 pages, LaTeX2e with jltmac2e style. Final version, to appear in Journal of Lie Theory

References in corpus (1)

• Deformations of chiral algebras

Cited by in corpus (8)

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• Polynomial identities of bicommutative algebras, Lie and Jordan elements
• Natural differential operators and graph complexes
• Volume preservation of Butcher series methods from the operad viewpoint