M2-branes, 3-Lie Algebras and Plücker relations
نویسنده
چکیده
We solve the Jacobi identity of metric 3-Lie algebras for which an associated Lie algebra either does not admit bi-invariant 4-forms or it is the sum of up to three abelian directions and a semi-simple Lie algebra. In all cases, we find that the structure constants of the metric 3-Lie algebras are sums of orthogonal simple 4-forms verifying a conjecture in math/0211170. In particular, there is no metric 3Lie algebra associated to a u(N) Lie alebra 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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تاریخ انتشار 2008