Three Schur functor of universal enveloping pre-Lie algebra
Résumé
Recent work of the first author and Tamaroff implies that the embedding of the Lie operad into the operad of pre-Lie algebras has the PBW property, and consequently, a functorial PBW type theorem holds for universal enveloping pre-Lie algebras of Lie algebras, generalising Segal's PBW theorem. We compute the corresponding Schur functor in terms of combinatorics of rooted trees.