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The optical gain and the luminescence of an InGaN quantum well with quaternary AlInGaN barriers is studied theoretically. We calculated the non-Markovian optical gain and the luminescence for the strained-layer wurtzite quantum well taking into account of many-body effects. It is predicted that both optical gain and luminescence are enhanced significantly when aluminum and indium are introduced into the quaternary barrier composition. Adding the aluminum to the barrier will increase of the confinement potentials for electrons and holes, while the indium will reduce the biaxial strain, which in turn reduces the internal field caused by spontaneous polarization and piezoelectric effects.