127 citations · 194 across the 19 of their papers we have counts for
21 papers
SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle
Viktor Abramov, Olga Liivapuu
We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We…
Transposed Poisson superalgebra
Viktor Abramov, Olga Liivapuu
In this paper we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative s…
3-Lie Algebras, Ternary Nambu-Lie algebras and the Yang-Baxter equation
Viktor Abramov, Emanuele Zappala
We construct ternary self-distributive (TSD) objects from compositions of binary Lie algebras, -Lie algebras and, in particular, ternary Nambu-Lie algebras. We show that the str…
Ternary algebras associated with irreducible tensor representations of SO(3) and quark model
Viktor Abramov
We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associati…
Nambu-Poisson Bracket on Superspace
Viktor Abramov
We propose an extension of n-ary Nambu-Poisson bracket to superspace R^{n|m} and construct by means of superdeterminant a family of Nambu-Poisson algebras of even degree functions,…
Quantum super Nambu bracket of cubic supermatrices and 3-Lie superalgebra
Viktor Abramov
We construct the graded triple Lie commutator of cubic supermatrices, which we call the quantum super Nambu bracket of cubic supermatrices, and prove that it satisfies the graded F…