Associative ternary algebras and ternary Lie algebras at cube roots of unity

Anti Maria Aader, Viktor Abramov, Olga Liivapuu

We propose an approach to extending the concept of a Lie algebra to ternary structures based on $\ddot{I}‰$-symmetry, where $\ddot{I}‰$ is a primitive cube root of unity. We give a definition of…