A Hom-associative analogue of n-ary Hom-Nambu algebras

Abstract

It is shown that every n-ary totally Hom-associative algebra with equal twisting maps yields an n-ary Hom-Nambu algebra via an n-ary version of the commutator bracket. The class of n-ary totally Hom-associative algebras is shown to be closed under twisting by self-weak morphisms. Every multiplicative n-ary totally Hom-associative algebra yields a sequence of multiplicative totally Hom-associative algebras of exponentially higher arities. Under suitable conditions, an n-ary totally Hom-associative algebra gives an (n-k)-ary totally Hom-associative algebra.

arXiv comment15 pages

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Cited by in corpus (6)

• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras
• Hom-power associative algebras
• Hom-algebras via PROPs
• Quadratic $n$-ary Hom-Nambu algebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras