  At sufficiently low temperatures, many quantum effects, such as weak
localization, electron-electron interaction (EEI), and Kondo screening, can
lead to pronounced corrections to the semiclassical electron transport.
Although low temperature corrections to longitudinal resistivity, ordinary Hall
resistivity, or anomalous Hall resistivity are often observed, the corrections
to three of them have never been simultaneously detected in a single sample.
Here, we report on the observation of $\sqrt T$-type temperature dependences of
the longitudinal, ordinary Hall and AH resistivities at temperatures down to at
least 20 mK in $n$-type HgCr$_2$Se$_4$, a half-metallic ferromagnetic
semiconductor that can reach extremely low carrier densities. For the samples
with moderate disorder, the longitudinal and ordinary Hall conductivities can
be satisfactorily described by the EEI theory developed by Altshuler \textit{et
al.}, whereas the large corrections to AH conductivity are inconsistent with
the existing theory, which predicts vanishing and finite corrections to AH
conductivity for EEI and weak localization, respectively.
