Generalized bialgebras and triples of operads
Generalized bialgebras and triples of operads
复制标题
DOI：
10.24033/ast.790
复制
发表时间：
2006-11
期刊：
影响因子：
--
通讯作者：
J. Loday
中科院分区：
文献类型：
--
作者：
J. Loday
我们引入了广义双代数的概念，它包括经典的双代数（Hopf代数）和许多其他的概念。证明了在较弱的条件下，连通广义双代数完全由其本原部分决定。这个结构定理将经典的Poincar\'e-Birkhoff-Witt定理和Cartier-Milnor-摩尔定理推广到了一大类广义双代数.从技术上讲，我们的工作理论的运算，使我们能够给一个概念证明我们的主要定理。它统一了几个结果，推广PBW和CMM，分散在文献中。我们处理许多明确的例子，并提出了一些建议。
We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its primitive part. This structure theorem extends the classical Poincar\'e-Birkhoff-Witt theorem and the Cartier-Milnor-Moore theorem, valid for cocommutative bialgebras, to a large class of generalized bialgebras. Technically we work in the theory of operads which permits us to give a conceptual proof of our main theorem. It unifies several results, generalizing PBW and CMM, scattered in the literature. We treat many explicit examples and suggest a few conjectures.