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We classify Lie 3-algebras possessing an invariant lorentzian inner product.The indecomposable objects are in one-to-one correspondence with compact realforms of metric semisimple Lie algebras. We analyse the moduli space ofclassical vacua of the Bagger-Lambert theory corresponding to these Lie3-algebras. We establish a one-to-one correspondence between one branch of themoduli space and compact riemannian symmetric spaces. We analyse the asymptoticbehaviour of the moduli space and identify a large class of models with modulibranches exhibiting the desired N^{3/2} behaviour.

Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space