Many classes of active galactic nuclei (AGNs) have been observed and recorded since the discovery of Seyfert galaxies. In this paper, we examine the sample of luminous galaxies in the Baryon Oscillation Spectroscopic Survey. We find a potentially new observational class of AGNs, one with strong and broad Mg II λ2799 line emission, but very weak emission in other normal indicators of AGN activity, such as the broad-line Hα, Hβ, and the near-ultraviolet AGN continuum, leading to an extreme ratio of broad Hα/Mg II flux relative to normal quasars. Meanwhile, these objects' narrow-line flux ratios reveal AGN narrow-line regions with levels of activity consistent with the Mg II fluxes and in agreement with that of normal quasars. These AGN may represent an extreme case of the Baldwin effect, with very low continuum and high equivalent width relative to typical quasars, but their ratio of broad Mg II to broad Balmer emission remains very unusual. They may also be representative of a class of AGN where the central engine is observed indirectly with scattered light. These galaxies represent a small fraction of the total population of luminous galaxies ( 0.1%), but are more likely (about 3.5?times) to have AGN-like nuclear line emission properties than other luminous galaxies. Because Mg II is usually inaccessible for the population of nearby galaxies, there may exist a related population of broad-line Mg II emitters in the local universe which is currently classified as narrow-line emitters (Seyfert 2 galaxies) or low ionization nuclear emission-line regions.
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