Quantization of coboundary Lie bialgebras


We show that any coboundary Lie bialgebra can be quantized. For this, we prove that Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and 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.


Benjamin Enriquez

IRMA (CNRS) - Département de Mathématiques
Université de Strasbourg
7, rue R. Descartes
F-67 084 Strasbourg

Gilles Halbout

Département de Mathématiques
Université de Montpellier 2
CC 5149, Place Eugène Bataillon F-34095 Montpellier