  We argue that one can relax the requirements of the non-associative
three-algebras recently used in constructing D=3, N=8 superconformal field
theories, and introduce the notion of ``relaxed three-algebras''. We present a
specific realization of the relaxed three-algebras in terms of classical Lie
algebras with a matrix representation, endowed with a non-associative
four-bracket structure which is prescribed to replace the three-brackets of the
three-algebras. We show that both the so(4)-based solutions as well as the
cases with non-positive definite metric find a uniform description in our
setting. We discuss the implications of our four-bracket representation for the
D=3, N=8 and multi M2-brane theory and show that our setup can shed light on
the problem of negative kinetic energy degrees of freedom of the Lorentzian
case.

High Energy Physics - Theory