2-Local derivations of infinite-dimensional Lie algebras
Shavkat AyupovV. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 81, Mirzo Ulughbek Street, 100170, Tashkent, UzbekistanBakhtiyor YusupovNational University of Uzbekistan, 4, University Street, 100174, Tashkent, Uzbekistan
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Annotatsiya
In the present paper, we study 2-local derivations of infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations of the Witt algebra as well as of the positive Witt algebra and the classical one-sided Witt algebra are (global) derivations. We also give an example of an infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.
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