Local Derivations and Local Automorphisms of Arbitrary Finite-Dimensional Nilpotent Lie and Leibniz Algebras

We study local derivations and local automorphisms of finite-dimensional nilpotent complex Lie and right Leibniz algebras. We prove that every non-abelian Lie algebra in this class admits both a local derivation which is not a derivation and a local automorphism which is not an automorphism. The constructions use a derivation $D$ satisfying $0\ne D([L,L])\subseteq Z(L)$. For non-abelian right Leibniz algebras, both existence statements hold whenever the dimension is at most seven or the nilpotency class is at most four. We construct an eight-dimensional non-Lie algebra of class five satisfying $\LocDer(A)=\Der(A)$ and $\LocAut(A)=\Aut(A)$. Consequently, eight and five are the least possible dimension and nilpotency class, respectively, for either equality.