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Pre-Lie algebras and the rooted trees operad

Frederic Chapoton·Muriel Livernet
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Abstract

A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatorial description in terms of rooted trees of the operad associated to this type of algebras and prove that it is a Koszul operad.

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Frederic Chapoton, Muriel Livernet. 2000-06-29. Pre-Lie algebras and the rooted trees operad. https://arxiv.org/abs/math/0002069

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