Résumé
Drinfeld (Proceedings of the International Congress of Mathematics (Berkley, 1986), 1987, pp. 798–820) constructs a quantum formal series Hopf algebra (QFSHA)
U′
h
starting from a quantum universal enveloping algebra (QUEA)
U
h
. In this paper, we prove that if (
U
h
,
R) is any quasitriangular QUEA, then (
U′
h
,Ad(
R)|
U′
h
⊗
U′
h
) is a braided QFSHA. As a consequence, we prove that if
g
is a quasitriangular Lie bialgebra over a field
k of characteristic zero and
g
∗
is its dual Lie bialgebra, the algebra of functions
F〚
g
∗〛
on the formal group associated to
g
∗
is a braided Hopf algebra. This result is a consequence of the existence of a quasitriangular quantization (
U
h
,
R) of
U(
g)
and of the fact that
U′
h
is a quantization of
F〚
g
∗〛
.