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

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

2005-09-13

arxiv.org/abs/math/0509293v3

Mathematics

Algebraic Topology

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

Scientific paper

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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