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Analogs of the cartan criteria forn-Lie algebras

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Abstract

It is shown that Cartan's criteria for finite-dimensional Lie algebras to be semisimple and solvable are fully adaptable to n-Lie algebras, provided that ideals of an n-Lie algebra are understood to be solvable in the sense of Kuz'min. Specifically, we present a characterization of the Kuz'min radical in terms of a trace form associated with some representation ρ, which is analogous to the characterization which we have in the case of Lie algebras. One more analog of the Cartan theorem is proved for n-Lie algebras which are solvable in the sense of Filippov.

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References

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Translated fromAlgebra i Logika, Vol. 34, No. 3, pp. 274-287, May-June, 1995.

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Kasymov, S.M. Analogs of the cartan criteria forn-Lie algebras. Algebr Logic 34, 147–154 (1995). https://doi.org/10.1007/BF02341871

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