Quantization of coboundary Lie bialgebras

Benjamin Enriquez (1) , Gilles Halbout (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We show that any coboundary Lie bialgebra can be quantized. For this, we prove that: (a) Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and (b) if such a quantization functor corresponds to an even associator, then it is also compatible with the operation of taking coopposites. We also use the relation between the Etingof-Kazhdan construction of quantization functors and the alternative approach to this problem, which was established in a previous work.

Domaines: Algèbres quantiques [math.QA]

Benjamin Enriquez, Gilles Halbout. Quantization of coboundary Lie bialgebras. 2007. ⟨hal-00203468⟩