LOCAL DERIVATIONS ON SOLVABLE LIE ALGEBRAS WITH A FILIFORM NILRADICAL

The present paper is devoted to the description of local derivations on rank one or zero solvable Lie algebras with the filiform nilradical. Firstly, we shall consider local derivations of rank one solvable Lie algebra  and  with the filiform nilradical  and  Namely, we find a general form of local derivations in the case of solvable Lie algebras whose nilradical is the Witt algebra  and special filiform algebra  In particular, in these cases the spaces  are Lie algebras. Finally, we shall find a general form of rank zero solvable Lie algebra with a metabelian filifrom nilradical.