6 citations · 6 across the 3 of their papers we have counts for
4 papers
Families of algebraic structures
Loic Foissy, Dominique Manchon, Yuanyuan Zhang
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the se…
Free pre-Lie family algebras
Dominique Manchon, Yuanyuan Zhang
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 algeb…
Free Rota-Baxter family algebras and Free (tri)dendriform family algebras
Yuanyuan Zhang, Xing Gao, Dominique Manchon
In this paper, we first construct the free Rota-Baxter family algebra generated by some set in terms of typed angularly -decorated planar rooted trees. As an application, we…
Free (tri)dendriform family algebras
Yuanyuan Zhang, Xing Gao, Dominique Manchon
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 al…