Let
S=k[
x
1
,...,
x
n
]
be a polynomial ring over a field
k
and
I
a monomial ideal of
S
. It is well known that the Poincaré series of
k
over
S/I
is rational. We describe the coefficients of the denominator of the series and study the multigraded homotopy Lie algebra of
S/I
.