  We present the first -- of a series -- study of the evolution of galaxies in
compact groups over the past 3 Gyr. This paper focuses on the evolution of the
nuclear activity and how it has been affected by the dense environment of the
groups. Our analysis is based on the largest multiwavelength compact group
sample to-date, containing complete ultraviolet-to-infrared (UV-to-IR)
photometry for 1,770 isolated groups (7,417 galaxies). We classified the
nuclear activity of the galaxies based on optical emission line and
mid-infrared diagnostic methods, as well as using spectral energy distribution
fitting. We observe a 15% increase on the number of the AGN-hosting late-type
galaxies found in dynamically old groups, over the past 3 Gyr, accompanied by
the corresponding decrease of their circumnuclear star formation. Comparing our
compact group results with those of local isolated field and interacting pair
galaxies, we find no differences in the AGN at the same redshift range. Based
on both optical and mid-IR colour classifications, we report the absence of
Seyfert 1 nuclei and we attribute this to the low accretion rates, caused by
the depletion of gas. We propose that the observed increase of LINER and
Seyfert 2 nuclei (at low-z's), in the early-type galaxies of the dynamically
young groups, is due to the morphological transformation of lenticular into
elliptical galaxies. Finally, we show that at any given stellar mass, galaxies
found in dynamically old groups are more likely to host an AGN. Our findings
suggest that the depletion of gas, due to past star formation and tidal
stripping, is the major mechanism driving the evolution of the nuclear activity
in compact groups of galaxies.
