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.
2009
Ardizzoni, Alessandro; Menini, Claudia; Stefan, Dragos
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/530052
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