# A distinguished example of filiform deformation

## TL;DR

This paper presents a specific 13-dimensional filiform complex Lie algebra with all codimension-1 ideals being characteristically nilpotent and demonstrates a non-trivial deformation of this algebra.

## Contribution

It provides a unique example of a high-dimensional filiform Lie algebra with special nilpotency properties and constructs its non-trivial deformation.

## Key findings

- Example of a 13-dimensional filiform Lie algebra with all codimension-1 ideals characteristically nilpotent
- Construction of a non-trivial filiform deformation of this algebra
- Insight into the structure and deformation theory of complex Lie algebras

## Abstract

We exhibit an example of a filiform (complex) Lie algebra of dimension 13 with all its ideals of codimension 1 being characteristically nilpotent, and we construct a non trivial filiform deformation of it.