Pre-Lie algebras and the rooted trees operad

A pre-Lie algebra is a vector space L endowed with a bilinear product ⋅:L×L→L satisfying the relation (x⋅y)⋅z−x⋅(y⋅z)=(x⋅z)⋅y−x⋅(z⋅y), ∀ x,y,z∈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 op... View More