  We classify, in a group theoretical manner, the BPS configurations in the
multiple M2-brane theory recently proposed by Bagger and Lambert. We present
three types of BPS equations preserving various fractions of supersymmetries:
in the first type we have constant fields and the interactions are purely
algebraic in nature; in the second type the equations are invariant under
spatial rotation SO(2), and the fields can be time-dependent; in the third
class the equations are invariant under boost SO(1,1) and provide the
eleven-dimensional generalizations of the Nahm equations. The BPS equations for
different number of supersymmetries exhibit the division algebra structures:
octonion, quarternion or complex.
