  The assembly of galaxies over cosmic time is tightly connected to the
assembly of their host dark matter halos. We investigate the stellar mass
growth history and the chemical enrichment history of central galaxies in
SDSS-MaNGA. We find that the derived stellar metallicity of passive central
galaxies is always higher than that of the star-forming ones. This stellar
metallicity enhancement becomes progressively larger towards low-mass galaxies
(at a given epoch) and earlier epochs (at a given stellar mass), which suggests
strangulation as the primary mechanism for star formation quenching in central
galaxies not only in the local universe, but also very likely at higher
redshifts up to $z\sim3$. We show that at the same present-day stellar mass,
passive central galaxies assembled half of their final stellar mass $\sim 2$
Gyr earlier than star-forming central galaxies, which agrees well with
semi-analytic model. Exploring semi-analytic model, we find that this is
because passive central galaxies reside in, on average, more massive halos with
a higher halo mass increase rate across cosmic time. As a consequence, passive
central galaxies are assembled faster and also quenched earlier than their
star-forming counterparts. While at the same present-day halo mass, different
halo assembly history also produces very different final stellar mass of the
central galaxy within, and halos assembled earlier host more massive centrals
with a higher quenched fraction, in particular around the "golden halo mass" at
$10^{12}\mathrm{M_\odot}$. Our results call attention back to the dark matter
halo as a key driver of galaxy evolution.
