This paper reviews the properties and applications of certain n-ary generalizations of Lie
algebras in a self-contained and unified way. These generalizations are algebraic structures …

The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary
algebras of Lie type including n-ary Nambu algebras, n-ary Nambu–Lie algebras and n-ary …

We discuss certain ternary algebraic structures appearing more or less naturally in various
domains of theoretical and mathematical physics. Far from being exhaustive, this article is …

The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has
become increasingly important in physics, and it should therefore be of interest to study the …

As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical
contexts, it is interesting to study general ways of constructing explicit realizations of such …

Beginning around the year 1980, the topic of approximate homomorphisms and derivations
and their stability theory in the field of functional equations and inequalities was taken up by …

In recent years it was argued that the underlying fundamental physical principle behind
string theory, not unlike the principle of equivalence and general covariance in Einstein's …

Let A be a Banach ternary algebra over a scalar field R or C and X be a ternary Banach A-
module. A linear mapping D:(A,[] A)→(X,[] X) is called a ternary Jordan derivation if D ([xxx] …

In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in $ C^* $-
ternary algebras and of bi-derivations on $ C^* $-ternary algebras for the following bi …

In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A
construction of the free involutive hom-associative color algebra on a hom-module is …