A Combinatorial Basis for the Free Lie Algebra of the Labelled Rooted Trees
نویسنده
چکیده
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 T = Lie ◦ F for some 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 .
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تاریخ انتشار 2007