论文标题
免费的前家庭代数
Free pre-Lie family algebras
论文作者
论文摘要
在本文中，我们首先定义了与树突状家族代数相关的前lie家族代数，如果是交换性的半群。然后，我们通过键入的装饰有根的树木构建一个前家庭代数，我们证明了这个前家庭代数的烦恼。我们还根据典型的标记生根树建造了前家族的奥尔特尔，并且我们获得了前lie家族代数的作业对类型标记的植根树的遗物是同构的，这概述了F. apkoton和M. Livernet的结果。最后，我们构建了Zinbiel和Preisson家族代数，并概括了M. Aguiar的结果。
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 F. Chapoton and M. Livernet. In the end, we construct Zinbiel and pre-Poisson family algebras and generalize results of M. Aguiar.
