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This paper is devoted to study 2-local derivations on Formula: see text-algebra Formula: see text which is an infinite-dimensional Lie algebra with some outer derivations. We prove that all 2-local derivations on the Formula: see text-algebra Formula: see text are derivations. We also give a complete classification of the 2-local derivation on the so-called thin Lie algebra and prove that it admits many 2-local derivations which are not derivations.
Xiaomin Tang (2020) studied this question.