On Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and   their Classification
  We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter content and couplings. We explore the relations of these actions with the N=2 actions based on generalized 3-Lie algebras found earlier and relate them to the original Bagger-Lambert-Gustavsson action. 
Sergey A. Cherkis, Vladimir Dotsenko and Christian Saemann