We show that, having a Hom-Lie algebra and an element of its dual vector space that
satisfies certain conditions, one can construct a ternary totally skew-symmetric bracket and …

The purpose of this paper is to study the relationships between a BiHom-Lie superalgebras
and its induced 3-BiHom-Lie superalgebras. We introduce the notion of (α s, β r) …

We consider a method that allows to construct the 3-Lie algebra if we have a Lie algebra
equipped with an analogue of the notion of trace. At the same time, it is well known that …

We show that given a Lie superalgebra and an element of its dual space, one can construct
the 3-Lie superalgebra. We apply this approach to Lie superalgebra of (m, n)-block matrices …

We construct 3-Lie superalgebras on a commutative superalgebra by means of involution
and even degree derivation. We construct a representation of induced 3-Lie algebras and …

In the present paper we give a survey of methods for constructing ternary Lie algebras and
ternary Lie superalgebras. We also propose a generalization of Nambu-Hamilton equation …

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 …

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 …

Complete hom-Lie superalgebras are considered and some equivalent conditions for a hom-
Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the …

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 …