Free pre-Lie family algebras
Yuanyuan Zhang
Henan University, Kaifeng, ChinaDominique Manchon
CNRS–Université Clermont-Auvergne, Aubière, France
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Abstract
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