  We construct the totally antisymmetric structure constants f^{ABCD} of a
3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary
semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write
down a maximally superconformal 3d theory that incorporates the expected
degrees of freedom of multiple M2 branes, including the "center-of-mass" mode
described by free scalar and fermion fields. The gauge field sector reduces to
a three dimensional BF term, which underlies the gauge symmetry of the theory.
We comment on the issue of unitarity of the quantum theory, which is
problematic, despite the fact that the specific form of the interactions
prevent the ghost fields from running in the internal lines of any Feynman
diagram. Giving an expectation value to one of the scalar fields leads to the
maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1)
multiplets, one of them ghost-like, which is decoupled at large g_YM.
