  We explore how the co-evolution of massive black holes (MBHs) and galaxies is
affected by environmental effects, addressing in particular MBHs hosted in the
central galaxies of clusters (we will refer to these galaxies in general as
'CGs'). Recently the sample of MBHs in CGs with dynamically measured masses has
increased, and it has been suggested that these MBH masses (M_BH) deviate from
the expected correlations with velocity dispersion (sigma) and mass of the
bulge (M_bulge) of the host galaxy: MBHs in CGs appear to be `over-massive'.
This discrepancy is more pronounced when considering the M_BH-sigma relation
than the M_BH-M_bulge one. We show that this behavior stems from a combination
of two natural factors, (i) that CGs experience more mergers involving
spheroidal galaxies and their MBHs, and (ii) that such mergers are
preferentially gas-poor. We use a combination of analytical and semi-analytical
models to investigate the MBH-galaxy co-evolution in different environments and
find that the combination of these two factors explains the trends observed in
current data-sets.
