Free pre-Lie family algebras

  • Yuanyuan Zhang

    Henan University, Kaifeng, China
  • Dominique Manchon

    CNRS–Université Clermont-Auvergne, Aubière, France
Free pre-Lie family algebras cover
Download PDF

This article is published open access under our Subscribe to Open model.


In this paper, we first define the pre-Lie family algebra associated to a dendriform family algebra in the case of a commutative semigroup. Then we construct a pre-Lie family algebra via typed decorated rooted trees, and we prove the freeness of this pre-Lie family algebra. We also construct pre-Lie family operad in terms of typed labeled rooted trees, and we obtain that the operad of pre-Lie family algebras is isomorphic to the operad of typed labeled rooted trees, which generalizes the result of Chapoton and Livernet. In the end, we construct Zinbiel and pre-Poisson family algebras and generalize results of Aguiar.

Cite this article

Yuanyuan Zhang, Dominique Manchon, Free pre-Lie family algebras. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 11 (2024), no. 2, pp. 331–361

DOI 10.4171/AIHPD/162