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Journal of Lie Theory 17 (2007), No. 2, 241--261
Copyright Heldermann Verlag 2007

Lie Elements in Pre-Lie Algebras, Trees and Cohomology Operations

Martin Markl
Mathematical Institute, Czech Academy of Sciences, Zitná 25, 11567 Praha 1, Czech Republic

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.

Keywords: Cohomology operations, pre-Lie algebras, Chevalley-Eilenberg complex.

MSC: 17B01, 17B56

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