论文标题
广义树突代数和打字的二进制树
Generalized dendrifom algebras and typed binary trees
论文作者
论文摘要
在这里，我们既统一并概括）在打字的二进制树上的非缔合结构，也就是说，平面二进制树的边缘是由集合$ω$的元素装饰的。我们证明，如果$ω$具有满足某些公理（EDS公理）的四种产品，包括Diassociative semigroup的公理。这包括由张，高和郭引入的匹配的树突状代数，以及与张，高和曼昌引入的半群相关的家族树突状代数，当然，当$ω$还原为单个元素时，当然还有Dendriform代数。我们还举例说明了ED的例子，包括第二个基数二进制ED；对类型二进制树上这种结构的产品的组合描述，也可以在文字上进行。一项研究相关作战的Koszul双重的研究；并考虑了共同体的存在，以获得树突状的双gebras。
We here both unify and generalize nonassociative structures on typed binary trees, that is to say plane binary trees which edges are decorated by elements of a set $Ω$. We prove that we obtain such a structure, called an $Ω$-dendriform structure, if $Ω$ has four products satisfying certain axioms (EDS axioms), including the axioms of a diassociative semigroup. This includes matching dendriform algebras introduced by Zhang, Gao and Guo and family dendriform algebras associated to a semigroup introduced by Zhang, Gao and Manchon , and of course dendriform algebras when $Ω$ is reduced to a single element. We also give examples of EDS, including all the EDS of cardinality two; a combinatorial description of the products of such a structure on typed binary trees, but also on words; a study of the Koszul dual of the associated operads; and considerations on the existence of a coproduct, in order to obtain dendriform bialgebras.
