This paper is devoted to study 2-local derivations on W-algebra W(2, 2) which is an infinite-dimensional Lie algebra with some outer derivations. We prove that all 2-local derivations on the W-algebra W(2, 2) 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.

中文翻译：

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W-代数 W(2,2) 上的 2-局部推导

本文致力于研究 2-local derivations onW-代数W(2, 2)这是一个具有一些外推导的无限维李代数。我们证明了所有 2 局部推导W-代数W(2, 2)是推导。我们还对所谓的薄李代数上的 2 局部导数给出了完整的分类，并证明它承认许多不是导数的 2 局部导数。