On the structure of cofree Hopf algebras
On the structure of cofree Hopf algebras
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DOI：
10.1515/crelle.2006.025
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发表时间：
2004-05
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影响因子：
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通讯作者：
J. Loday;Maria O. Ronco
中科院分区：
文献类型：
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作者：
J. Loday;Maria O. Ronco
本文证明了非余交换Hopf代数的Poincaré-Birkhoff-Witt定理和Cartier-Milnor-摩尔定理的一个类似定理。上自由霍普夫代数的本原部分是非微分B ∞-代数。构造了一个从非微分B ∞-代数到2-结合代数（即具有两个结合运算的代数）的泛包络函子U 2.我们证明了任何余自由Hopf代数都是U2（Prim）形式的.利用平面树对自由2as-代数的描述，我们解开了非微分B ∞-代数的运算.
Abstract We prove an analogue of the Poincaré-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a nondifferential B ∞-algebra. We construct a universal enveloping functor U2 from nondifferential B ∞-algebras to 2-associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra ℋ is of the form U2(Prim ℋ). We take advantage of the description of the free 2as-algebra in terms of planar trees to unravel the operad associated to nondifferential B ∞-algebras.