2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58658A 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.13 pages, uses xypic, typos corrected and more explicit description of the free algebraQuantum AlgebraRings and Algebras18D50; 17B60; 17D65; 05C05text