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.