A pr 2 00 8 M 2-branes , 3-Lie Algebras and Plücker relations

  title={A pr 2 00 8 M 2-branes , 3-Lie Algebras and Pl{\"u}cker relations},
  author={George Papadopoulos},
We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no metric 3-Lie algebra associated to a u(N) Lie algebra for N > 2. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras. 
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Gauge Symmetry and Supersymmetry of Multiple M2- Branes

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