Viktor Abramov

collaborators

3 papers

math.RA2025

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 $I ¨ $ -symmetry, where $I ¨ $ is a primitive cube root of unity. We give a definition of…

math-ph2025

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…

math.DG2025

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…