4 problems

Let $G$ be a solvable Lie group. A complete left-invariant affine structure on $G$ is a left-invariant flat and torsion-free affine connection whose associated affine structure is…

Let $\mathcal A$ be a complete abelian left-symmetric algebra (LSA) with a nondegenerate Hessian-type inner product. Let $\operatorname{sDer}(\mathcal A)$ denote its space of infin…

Existence conjecture. Every nilpotent Lie algebra over $\mathbb{C}$ admits an LSA structure.

Let $G$ be a nilpotent Lie group acting simply transitively on $\mathbb{R}^{n}$ by affine transformations. A central translation conjecture. Every such group $G$ contains a transla…