Abstract
We study naturally graded filiform \( n \)-Lie algebras. Among these algebras, we distinguish some algebra with the simplest structure that is an analog of the model filiform Lie algebra. We describe the derivations of the algebra and obtain the classification of solvable \( n \)-Lie algebras whose maximal hyponilpotent ideal coincides with the distinguished naturally graded filiform algebra. Furthermore, we show that these solvable \( n \)-Lie algebras possess outer derivations.
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The authors are deeply grateful to the referee for the valuable recommendations and suggestions for improving the final version of the article.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 3–22. https://doi.org/10.33048/smzh.2022.63.101
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Abdurasulov, K.K., Gaybullaev, R.K., Omirov, B.A. et al. Maximal Solvable Extension of Naturally Graded Filiform \( n \)-Lie Algebras. Sib Math J 63, 1–18 (2022). https://doi.org/10.1134/S0037446622010013
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DOI: https://doi.org/10.1134/S0037446622010013
Keywords
- \( n \)-Lie algebra
- Filippov algebra
- nilpotent \( n \)-algebra
- hyponilpotent ideal of an \( n \)-algebra
- solvable \( n \)-algebra
- derivation
- characteristic sequence
- graded algebra