On $n$ -ary Lie algebras of type $(r,l)$

preprint2015arXivOpen access

These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M.Vinogradov and M.M.Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple $n$ -ary Lie algebras of type $(n-1,l)$ for $l>0$ .

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On $n$ -ary Lie algebras of type $(r,l)$

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On nnn-ary Lie algebras of type (r,l)(r,l)(r,l)

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On $n$ -ary Lie algebras of type $(r,l)$