Résumé
Let
(
g
,
δ
ℏ
)
be a Lie bialgebra. Let
(
U
ℏ
(
g
)
,
Δ
ℏ
)
a quantization of
(
g
,
δ
ℏ
)
through Etingof–Kazhdan functor. We prove the existence of a
L
∞
-morphism between the Lie algebra
C
(
g
)
=
Λ
(
g
)
and the tensor algebra (without unit)
T
+
U
=
T
+
(
U
ℏ
(
g
)
[
−
1
]
)
with Lie algebra structure given by the Gerstenhaber bracket. When
s is a twist for
(
g
,
δ
)
, we deduce from the formality morphism the existence of a quantum twist
F. When
(
g
,
δ
,
r
)
is a coboundary Lie bialgebra, we get the existence of a quantization
R of
r.