1 citations · 1 across the 5 of their papers we have counts for
5 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…
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…
Algebras with ternary law of composition combining Z_2 and Z_3 gradings
V. Abramov, R. Kerner, O. Liivapuu
In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with…
Algebras with ternary law of composition and their realization by cubic matrices
V. Abramov, R. Kerner, O. Liivapuu +1
We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple…