Let
L
L
denote the simple Lie algebra
sl(2,
C
)
{\text {sl(2,}}{\mathbf {C}}{\text {)}}
over the complex numbers
C
{\mathbf {C}}
. For any simple
L
L
-modules
S
S
, considered as a left unital module over the universal enveloping algebra of
L
,
U
(
L
)
L,U(L)
, the injective hull of
S
,
E
L
(
S
)
S,{E_L}(S)
, is a locally Artinian
U
(
L
)
U(L)
-module.