Local derivations on solvable Lie algebras of maximal rank
Abstract
The present paper is devoted to the description of local derivations on solvable Lie algebras of maximal rank. Namely, we consider a solvable Lie algebra of the form R=Q⊕N, where Q is the maximal torus subalgebra of R, N is the nilradical of R and dim Q=dim N/N2. We prove that any local derivation of such solvable Lie algebra R is a derivation.Further, we present two examples of solvable Lie algebras which satisfy the condition dim Q<dim N/N2 and the first algebra admit a local derivation which is not a derivation, while for the second algebra we prove that any local derivation is a derivation. We also apply the main result of the paper to the description of local derivations on so-called standard Borel subalgebras of complex simple Lie algebras.