Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals whose maximal complemented space of its nilradical

Abstract

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded p-filiform non-Lie Leibniz algebra (n − p ≥ 4) and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras.

On some solvable Leibniz algebras and their completeness

“…Let us denote by R(N, m) the class of maximal (with respect to the dimension) solvable Leibniz algebras whose nilradical is N , that is, the class of solvable Leibniz algebras whose nilradical is N and maximal possible codimension of the nilradical is m. In [3] it was proved that for the nilpotent Leibniz algebra N = µ 1 the value of m is equal to k and the description of R(µ 1 , k) was given as follows.…”

Leibniz algebras whose solvable ideal is the maximal extension of the nilradical

“…Such algebras are also important from a cohomological point of view and many complete Leibniz algebras belong to the class of cohomologically rigid algebras. Later J.K. Adashev and others [3] showed that solvable Leibniz algebra with nilradical being naturally graded p-filiform Leibniz algebra of maximal codimension is complete. Moreover, B.A.…”