Free (tri)dendriform family algebras

Dominique Manchon (1) , Gao Xing (2) , Yuanyuan Zhang (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Department of Mathematics and Statistics [Lanzhou]

In this paper, we first prove that a Rota-Baxter family algebra indexed by a semigroup induces an ordinary Rota-Baxter algebra structure on the tensor product with the semigroup algebra. We show that the same phenomenon arises for dendriform and tridendriform family algebras. Then we construct free dendriform family algebras in terms of typed decorated planar binary trees. Finally, we generalize typed decorated rooted trees to typed valently decorated Schröder trees and use them to construct free tridendriform family algebras.

Mots clés: Rota-Baxter algebra; Rota-Baxter family algebra; (tri)dendriform algebra; (tri)dendriform family algebra; typed decorated planar binary trees; typed valently decorated rooted trees

Domaines: Mathématiques [math]; Combinatoire [math.CO]

Dominique Manchon, Gao Xing, Yuanyuan Zhang. Free (tri)dendriform family algebras. Journal of Algebra, 2020, ⟨10.1016/978-3-030-37030-5⟩. ⟨hal-02404042⟩