Local and 2-local 12-derivations of infinite-dimensional Lie algebras

In this work, we describe local and 2-local [Formula: see text]-derivations of infinite-dimensional Lie algebras. We prove that all local and 2-local [Formula: see text]-derivations of the Witt algebra as well as of the positive Witt algebra and the classical one-sided Witt algebra are [Formula: see text]-derivations. We also give an example of an infinite-dimensional Lie algebra with a local (2-local) [Formula: see text]-derivation which is not a [Formula: see text]-derivation. Further we prove that all local (2-local) [Formula: see text]-derivations on the [Formula: see text] algebra are [Formula: see text]-derivations.