Pre-Lie algebras and the rooted trees operad

Details Pre-Lie algebras and the rooted trees operad Pre-Lie algebras and the rooted trees operad

2000-02-10

arxiv.org/abs/math/0002069v2

IMRN 2001 vol. 8 p 395-408

Mathematics

Quantum Algebra

13 pages, uses xypic, typos corrected and more explicit description of the free algebra

Scientific paper

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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