arXiv subjects
Publications and source records attributed to Abdellatif Saidi.
We define a family of multigraded operads $O_λ$ depending on a scalar parameter, such that forgetting the multigraduation gives back the pre-Lie operad when the parameter $λ$ is equal to one, and the NAP operad governing Non-Associative Permutative algebras when $λ$ is equal to zero.
D. Calaque, K. Ebrahimi-Fard and D. Manchon have recently defined a Hopf algebra by introducing a new coproduct on a commutative algebra of rooted forests. The space of primitive elements of the graded dual is endowed with a left pre-Lie product defined in terms of insertion of a tree inside another. In this work we prove a ``derivation'' relation between this pre-Lie structure and the left pre-Lie product defined by grafting.