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

Martin Markl
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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.

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Martin Markl. 2006-07-18. Lie elements in pre-Lie algebras, trees and cohomology operations. https://arxiv.org/abs/math/0509293

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