On solvable Leibniz algebras whose nilradical is a direct sum of null-filiform algebras

Abstract

In this paper, we continue the investigation of complex finite-dimensional solvable Leibniz algebras with nilradical , where are ideals of maximal nilindex of the nilradical. The multiplication tables of such solvable algebras with restrictions to structural constants are obtained. In the case when the complemented space to the nilradical is one-dimensional, we present a multiplication table without any restrictions to structural constants. The classification of solvable Leibniz algebras, whose dimension of the complemented vector space to the nilradical is equal to s, is also given. Moreover, the description of solvable Leibniz algebras with the condition of each is ideal of the algebra is presented.

Keywords:

• Leibniz algebra
• solvability
• nilpotency
• nilradical
• derivation
• null-filiform Leibniz algebra

AMS Subject Classifications:

• 17A32
• 17A36
• 17A60
• 17A65
• 17B30

Notes

The second author was supported by Ministerio de Ciencia e Innovación (European FEDER support included) [grant number MTM2009-14464-C02-01]. The third author was partially supported by the Grant (RGA) No:11-018 RG/Math/AS_I–UNESCO FR: 3240262715.