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- Title
Free pre-Lie family algebras.
- Authors
Yuanyuan Zhang; Manchon, Dominique
- 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.
- Subjects
COMMUTATIVE algebra; ALGEBRA; FAMILIES; YANG-Baxter equation
- Publication
Annales de l'Institut Henri Poincaré D, 2024, Vol 11, Issue 2, p331
- ISSN
2308-5827
- Publication type
Article
- DOI
10.4171/AIHPD/162