4 papers
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 -symmetry, where is a primitive cube root of unity. We give a definition of a…
Odd and even derivations, transposed Poisson superalgebra and 3-Lie superalgebra
Viktor Abramov, Nikolai Sovetnikov
One important example of a transposed Poisson algebra can be constructed by means of a commutative algebra and its derivation. This approach can be extended to superalgebras, that…
Ternary associator, ternary commutator and ternary Lie algebra at cube roots of unity
Viktor Abramov
We extend the concepts of the associator and commutator from algebras with a binary multiplication law to algebras with a ternary multiplication law using cube roots of unity. By a…
Ternary Associativity and Ternary Lie Algebra at Cube Root of Unity
Viktor Abramov
We propose a new approach to extending the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on ternary associativity of the…