Local and 2-local 12-derivations on finite-dimensional Lie algebras

In this work, we introduce the notion of local and 2-local -derivations and describe local and 2-local 12-derivation of finite-dimensional solvable Lie algebras with filiform, Heisenberg, and abelian nilradicals. Moreover, we describe the local 12-derivation of oscillator Lie algebras, Schr\"odinger algebras, and Lie algebra with a three-dimensional simple part, whose radical is an irreducible module. We prove that an algebra with only trivial 12-derivation does not admit local and 2-local 12-derivation, which is not 12-derivation.