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

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

2010-05-13

arxiv.org/abs/1005.2373v1

Mathematics

Rings and Algebras

15 pages

Scientific paper

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.

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