  We present the discovery of rare active galactic nuclei (AGNs) in nearby (z <
0.05) compact elliptical galaxies (cEs) located in isolated environments. Using
spectroscopic data from the Sloan Digital Sky Survey (SDSS) Data Release 12,
four AGNs were identified based on the optical emission-line diagnostic
diagram. SDSS optical spectra of AGNs show the presence of distinct narrow-line
emissions. Utilizing the black hole (BH) mass-stellar velocity dispersion
scaling relation and the correlation between the narrow L([OIII])/L(H\b{eta})
line ratio and the width of the broad H{\alpha} emission line, we estimated the
BH masses of the cEs to be in the range of 7 x 10^5 - 8 x 10^7 Msun. The
observed surface brightness profiles of the cEs were fitted with a double
Sersic function using the Dark Energy Camera Legacy Survey r-band imaging data.
Assuming the inner component as the bulge, the K-band bulge luminosity was also
estimated from the corresponding Two Micron All Sky Survey images. We found
that our cEs follow the observed BH mass-stellar velocity dispersion and BH
mass-bulge luminosity scaling relations, albeit there was a large uncertainty
in the derived BH mass of one cE. In view of the observational properties of
BHs and those of the stellar populations of cEs, we discuss the proposition
that cEs in isolated environments are bona fide low-mass early-type galaxies
(i.e., a nature origin).
