Constraining Maximally Supersymmetric Membrane Actions
  We study the recent construction of maximally supersymmetric field theory Lagrangians in three spacetime dimensions that are based on algebras with a triple product. Assuming that the algebra has a positive definite metric compatible with the triple product, we prove that the only non-trivial examples are either the well known case based on a four dimensional algebra or direct sums thereof. 
Jerome P. Gauntlett, Jan B. Gutowski