Maximal Solvable Extension of Naturally Graded Filiform $ n $-Lie Algebras
K. K. AbdurasulovR. K. GaybullaevNational University of Uzbekistan, Tashkent, UzbekistanB. A. OmirovNational University of Uzbekistan, Tashkent, UzbekistanAbror Khudoyberdiyev
ABI
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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