Maximal solvable extension of naturally graded filiform $n$-Lie algebras

K. K. Abdurasulov^a, R. K. Gaybullaev^b, B. A. Omirov^ab, A. Kh. Khudoyberdiyev<sup>ba

a</sup> V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan
^b National University of Uzbekistan named after M. Ulugbek, Tashkent

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.

UDC: 512.554

Received: 11.05.2021
Revised: 26.10.2021
Accepted: 10.12.2021

DOI: 10.33048/smzh.2022.63.101

 English version: Siberian Mathematical Journal, 2022, 63:1, 1–18

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