Reduced Lie ternary algebras

We introduce a notion of variety of RLT-algebras as a variety of ternary anticommutative algebras such that the Jacobian $J(x,y,z;u,v)$ (see (3)) is skew-symmetric in all the arguments. The algebras in this variety possess the property that their reduced algebra is a Lie algebra. We show that this variety properly contains the variety of Filippov algebras and coincides with the variety of Filippov algebras in the presence of a non-degenerate (skew)symmetric anti-invariant form. We also obtain some structure results on RLT-algebras.