A Milnor-moore Type Theorem for Braided Bialgebras
نویسندگان
چکیده
The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra A having a λ-cocommutative infinitesimal braiding for some regular element λ 6= 0 in the base field, then the infinitesimal braiding of A is of Hecke-type of mark λ and A is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.
منابع مشابه
Pbw Deformations of Braided Symmetric Algebras and a Milnor-moore Type Theorem for Braided Bialgebras
Braided bialgebras were defined by mimicking the definition of bialgebras in a braided category; see [Ta]. In this paper we are interested in those braided bialgebras that are connected as a coalgebra, and such that, up to multiplication by a certain scalar, their braiding restricted to the primitive part is a Hecke operator. To every braided bialgebra as above we associate a braided Lie algebr...
متن کاملand triples of operads
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 Poincaré-Birkhoff-Witt theorem and the Cartier-Milnor-Moore theorem, valid for cocommutative bia...
متن کاملBraided-Lie bialgebras associated to Kac–Moody algebras
Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of Kac–Moody bialgebras. Doing so, we obtain many new examples of infinite-dimensional braided-Lie bialgebras. We analyze further the case of untwist...
متن کاملCombinatorics of $φ$-deformed stuffle Hopf algebras
3 General results on summability and duality 4 3.1 Total algebras and duality . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Series and infinite sums . . . . . . . . . . . . . . . . . . . 4 3.1.2 Summable families in Hom spaces. . . . . . . . . . . . . . 5 3.1.3 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Theorem of Cartier-Quillen-Milnor-Moore (analytic form) . ....
متن کاملWeak Projections onto a Braided Hopf Algebra
We show that, under some mild conditions, a bialgebra in an abelian and coabelian braided monoidal category has a weak projection onto a formally smooth (as a coalgebra) sub-bialgebra with antipode; see Theorem 1.12. In the second part of the paper we prove that bialgebras with weak projections are cross product bialgebras; see Theorem 2.12. In the particular case when the bialgebra A is cocomm...
متن کامل