  We investigated AGN activity in low-mass galaxies, an important regime that
can shed light onto BH formation and evolution, and their interaction with
their host galaxies. We identified 336 AGN candidates from a parent sample of
$\sim 48,000$ nearby low-mass galaxies ($M_{\rm \star} \leq 10^{9.5}M_\odot$,
$z < 0.1$) in the SDSS. We selected the AGN using the classical BPT diagram, a
similar optical emission line diagnostic based on the HeII$\lambda$4686 line,
and mid-IR color cuts. Different criteria select host galaxies with different
physical properties such as stellar mass and optical color, and only 3 out of
336 sources fulfill all three criteria. This could be in part due to selection
biases. The resulting AGN fraction of $\sim 0.7 \%$ is at least one order of
magnitude below the one estimated for more massive galaxies. At optical
wavelengths, the HeII-based AGN selection appears to be more sensitive to AGN
hosted in star-forming galaxies than the classical BPT diagram, at least in the
low-mass regime. The archival X-ray and radio data available for some of the
optically selected AGN candidates seem to confirm their AGN nature, but
follow-up observations are needed to confirm the AGN nature of the rest of the
sample, especially in the case of mid-IR selection. Our sample will be
important for future follow-up studies aiming to understand the relation
between BHs and host galaxies in the low-mass regime.
