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