A combinatorial basis for the free Lie algebra of the labelled rooted trees
Rings and Algebras
2010-10-05 v1 Combinatorics
Abstract
The pre-Lie operad can be realized as a space T of labelled rooted trees. A result of F. Chapoton shows that the pre-Lie operad is a free twisted Lie algebra. That is, the S-module T is obtained as the plethysm of the S-module Lie with an S-module F. In the context of species, we construct an explicit basis of F. This allows us to give a new proof of Chapoton's results. Moreover it permits us to show that F forms a sub nonsymmetric operad of the pre-Lie operad T.
Keywords
Cite
@article{arxiv.0707.4460,
title = {A combinatorial basis for the free Lie algebra of the labelled rooted trees},
author = {Nantel Bergeron and Muriel Livernet},
journal= {arXiv preprint arXiv:0707.4460},
year = {2010}
}
Comments
12 pages, uses xypic