4 problems

Linear deformation conjecture. The algebra $\mathcal{L}$ is a linear deformation of the algebra $\mathcal{L}_s$ for certain $s \in \mathbb{N}^t$.

Affine-structure conjecture. For $n\ge 13$, these algebras do not admit any affine structure.

Scarcity conjecture. There are “a few” characteristically nilpotent algebras among the filiform Lie algebras.

Let $M_0$ be the model infinite filiform Lie algebra with basis $a,e_1,e_2,\ldots$, and let a deformation be specified by coefficients $\lambda_{js}$ in … for all $j\geq 1$, where…