On the Structure of Cofree Hopf Algebras
نویسنده
چکیده
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 B∞-algebra. We construct a universal enveloping functor U2 from 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(PrimH). We take advantage of the description of the free 2as-algebra in terms of planar trees to unravel the structure of the operad B∞.
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تاریخ انتشار 2004