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 $(A,\mathfrak{c}_A)$ which is infinitesimally $\lambda $-cocommutative for some element $\lambda \neq 0$ that is not a root of one in the base field, then the infinitesimal braiding of $A$ is of Hecke-type of mark $\lambda $ and $A$ is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.
Braided Bialgebras of Hecke-type
ARDIZZONI, Alessandro;MENINI, Claudia;STEFAN, Dragos
2009
Abstract
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 $(A,\mathfrak{c}_A)$ which is infinitesimally $\lambda $-cocommutative for some element $\lambda \neq 0$ that is not a root of one in the base field, then the infinitesimal braiding of $A$ is of Hecke-type of mark $\lambda $ and $A$ is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.File in questo prodotto:
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