We consider associative algebras with an action by derivations by some finite dimensional and semisimple Lie algebra. We prove that if a differential variety has almost polynomial growth, then it is generated by one of the algebras
U
T
2
(
W
λ
)
UT_2(W_\lambda )
or
E
n
d
(
W
μ
)
End(W_\mu )
for some integral dominant weight
λ
,
μ
\lambda ,\mu
with
μ
≠
0
\mu \neq 0
. In the special case
L
=
s
l
2
L=\mathfrak {sl}_2
we prove that this is a sufficient condition too.