Generalization of n-ary Nambu algebras and beyond
H. Ataguema, A. Makhlouf, S. Silvestrov

TL;DR
This paper introduces generalized n-ary Hom-algebra structures that encompass various n-ary algebras of Lie and associative types, providing a framework for constructing new examples from existing algebras and endomorphisms.
Contribution
It extends the theory of n-ary algebras by defining Hom-algebra structures that unify and generalize multiple existing algebraic systems, along with a method to generate examples.
Findings
Defined n-ary Hom-algebra structures generalizing existing n-ary algebras.
Provided a construction method for new examples from known n-ary algebras and endomorphisms.
Demonstrated the applicability of the framework through multiple examples.
Abstract
The aim of this paper is to introduce -ary Hom-algebra structures generalizing the -ary algebras of Lie type enclosing -ary Nambu algebras, -ary Nambu-Lie algebras, -ary Lie algebras, and -ary algebras of associative type enclosing -ary totally associative and -ary partially associative algebras. Also, we provide a way to construct examples starting from an -ary algebra and an -ary algebras endomorphism. Several examples could be derived using this process.
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