Resumen de Quantization of Lie bialgebras and shuffle algebras of Lie algebras

B. Enriquez

• To any field K of characteristic zero, we associate a set (K) and a group G0(K) . Elements of (K) are equivalence classes of families of Lie polynomials subject to associativity relations. Elements of G0(K) are universal automorphisms of the adjoint representations of Lie bialgebras over K . We construct a bijection between (K)×G0(K) and the set of quantization functors of Lie bialgebras over K . This construction involves the following steps.¶ 1) To each element ϖ of (K) , we associate a functor a↦Shϖ(a) from the category of Lie algebras to that of Hopf algebras...