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arXiv · 0812.4058

Generalization of n-ary Nambu algebras and beyond

H. Ataguema·A. Makhlouf·S. Silvestrov
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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.

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H. Ataguema, A. Makhlouf, S. Silvestrov. 2008-12-21. Generalization of n-ary Nambu algebras and beyond. https://doi.org/10.1063/1.3167801

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