Abstract In the present work, we compute quasi-derivations of the Witt algebra and some algebras well related to the Witt algebra. Namely, we prove that each quasi-derivation of the Witt algebra is a sum of a derivation and a 12 1 2 -derivation; a similar result is obtained for the Virasoro algebra. A different situation appears for Lie algebras W (a, b): W (a, b): In the case of b=-1, b = - 1, they do not have interesting examples of quasi-derivations, but the case of b -1 b ≠ - 1 provides some new non-trivial examples of quasi-derivations. We also completely describe all quasi-derivations of W (a, b). W (a, b). As a corollary, we describe the derivations and quasi-derivations of the Novikov–Witt and admissible Novikov–Witt algebras previously constructed by Bai and his co-authors; and δ -derivations and transposed δ -Poisson structures on cited Lie algebras. In particular, we proved that each W (a, b) W (a, b) admits a non-trivial transposed 11-b 1 1 - b -Poisson structure.
Kaygorodov et al. (2026) studied this question.