Pre-Lie algebras and the rooted trees operad
Quantum Algebra
2007-05-23 v2 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.math/0002069,
title = {Pre-Lie algebras and the rooted trees operad},
author = {Frederic Chapoton and Muriel Livernet},
journal= {arXiv preprint arXiv:math/0002069},
year = {2007}
}
Comments
13 pages, uses xypic, typos corrected and more explicit description of the free algebra