Generalization of n-ary Nambu algebras and beyond

Abstract

The aim of this paper is to introduce $n$-ary Hom-algebra structures generalizing the $n$-ary algebras of Lie type enclosing $n$-ary Nambu algebras, $n$-ary Nambu-Lie algebras, $n$-ary Lie algebras, and $n$-ary algebras of associative type enclosing $n$-ary totally associative and $n$-ary partially associative algebras. Also, we provide a way to construct examples starting from an $n$-ary algebra and an $n$-ary algebras endomorphism. Several examples could be derived using this process.

References in corpus (3)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Ternary algebras and groups

Cited by in corpus (12)

• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
• Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
• Hom-Novikov algebras
• Representations and module-extensions of hom 3-Lie algebras
• Some constructions of multiplicative $n$-ary Hom-Nambu algebras
• 3-ary Hom-Lie superalgebras induced Hom-Lie superalgebras
• Multi-parameter formal deformations of ternary hom-Nambu-Lie algebras
• Quadratic and symplectic structures on 3-(Hom)-$\rho$-Lie algebras
• Hyperpolyadic structures