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arXiv · 1401.1272

Asssociative algebras under multi-commutator

Askar Dzhumadil'daev
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Abstract

For an associative algebra $A$ a skew-symmetric sum of $n!$ products of $n$ elements of $A$ in all possible order is called $n$-commutator. We consider $A$ as $n$-ary algebra under $n$-commutator. We prove that it has an identity of $ω$-degree $2$ (namely, homotopical $n$-Lie identity) if $n$ is even and an identity of $ω$-degree $3$ if $n$ is odd.

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Askar Dzhumadil'daev. 2014-01-24. Asssociative algebras under multi-commutator. https://arxiv.org/abs/1401.1272

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