  We have studied low-temperature properties of interacting electrons in a
one-dimensional quantum wire (Luttinger liquid) side-hybridized with a
single-level impurity. The hybridization induces a back-scattering of electrons
in the wire which strongly affects its low energy properties. Using a one-loop
renormalization group approach valid for a weak electron-electron interaction,
we have calculated a transmission coefficient through the wire,
$\mathcal{T}(\varepsilon)$, and a local density of states, $\nu(\varepsilon)$
at low energies $\varepsilon $. In particular, we have found that the
antiresonance in $\mathcal{T}(\varepsilon)$ has a generalized Breit-Wigner
shape with the effective width $\Gamma(\varepsilon)$ which diverges at the
Fermi level.
