  Three-dimensional conformal theories with six supersymmetries and SU(4)
R-symmetry describing stacks of M2-branes are here proposed to be related to
generalized Jordan triple systems. Writing the four-index structure constants
in an appropriate form, the Chern-Simons part of the action immediately
suggests a connection to such triple systems. In contrast to the previously
considered three-algebras, the additional structure of a generalized Jordan
triple system is associated to a graded Lie algebra, which corresponds to an
extension of the gauge group. In this note we show that the whole theory with
six manifest supersymmetries can be naturally expressed in terms of such a
graded Lie algebra. Also the BLG theory with eight supersymmetries is included
as a special case.
