Quantization of Lie bialgebras and shuffle algebras of Lie algebras

• B. Enriquez ^[1]
  1. [1] Université Louis Pateur, Francia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 7, Nº. 3, 2001, págs. 321-407
• Idioma: inglés
• DOI: 10.1007/pl00001404
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• Resumen

  • 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...