Local and 2-local completeness of a class of single diamond thin Lie algebras

We introduce a class of single diamond thin Lie algebras 𝒯(Λ), where Λ is a sequence of nonzero complex numbers. Using the properties of index version of Pochhammer and combination symbols, we completely determine the local and 2-local derivations on 𝒯(Λ). We show that the codimension of the space of derivations on 𝒯(Λ) in the space of local derivations on 𝒯(Λ) is one, while that in the space of 2-local derivations on 𝒯(Λ) is infinite. These, in particular, imply that 𝒯(Λ) is both non-local complete and non-2-local complete.