Nonfiliform characteristically nilpotent Lie algebras

TL;DR

This paper constructs large families of nonfiliform characteristically nilpotent Lie algebras through deformations and central extensions, revealing their rigidity and structural properties.

Contribution

It introduces new methods for constructing nonfiliform characteristically nilpotent Lie algebras using deformations of specific Lie algebras and studies their cohomological and rigidity properties.

Findings

Constructed large families of such Lie algebras.

Identified conditions for rigidity of certain laws.

Demonstrated compatibility of deformations with central extensions.

Abstract

We construct large families of characteristically nilpotent Lie algebras by considering deformations of the Lie algebra g_{m,m-1}^{4} of type Q_{n},and which arises as a central extension fo the filiform Lie algebra L_{n}. By studying the graded cohomology spaces we obtain that the sill algebras are isomorphic to the nilradicals of solvable, complete Lie algebra laws. For extremal cocycles these laws are also rigid. Considering supplementary cocycles we construcy, for dimensions n>8, nonfiliform characteristically nilpotent Lie algebras and show that for certain deformations these are compatible with central extensions.