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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 1, Pages 3–22
DOI: https://doi.org/10.33048/smzh.2022.63.101 (Mi smj7638) 		 
Maximal solvable extension of naturally graded filiform $n$-Lie algebras

K. K. Abdurasulova, R. K. Gaybullaevb, B. A. Omirovab, A. Kh. Khudoyberdiyevba

a V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan
b National University of Uzbekistan named after M. Ulugbek, Tashkent
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DOI: https://doi.org/10.33048/smzh.2022.63.101
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.
Keywords: $n$-Lie algebra, Filippov algebra, nilpotent $n$-algebra, hyponilpotent ideal of an $n$-algebra, solvable $n$-algebra, derivation, characteristic sequence, graded algebra.
Received: 11.05.2021
Revised: 26.10.2021
Accepted: 10.12.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 1, Pages 1–18
DOI: https://doi.org/10.1134/S0037446622010013
Bibliographic databases:
Document Type: Article
UDC: 512.554
Language: Russian
Citation: K. K. Abdurasulov, R. K. Gaybullaev, B. A. Omirov, A. Kh. Khudoyberdiyev, “Maximal solvable extension of naturally graded filiform $n$-Lie algebras”, Sibirsk. Mat. Zh., 63:1 (2022), 3–22; Siberian Math. J., 63:1 (2022), 1–18
Citation in format AMSBIB
\Bibitem{AbdGayOmi22}
\by K.~K.~Abdurasulov, R.~K.~Gaybullaev, B.~A.~Omirov, A.~Kh.~Khudoyberdiyev
\paper Maximal solvable extension of naturally graded filiform $n$-Lie algebras
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 1
\pages 3--22
\mathnet{http://mi.mathnet.ru/smj7638}
\crossref{https://doi.org/10.33048/smzh.2022.63.101}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4440262}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 1
\pages 1--18
\crossref{https://doi.org/10.1134/S0037446622010013}
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