12 problems

Dimension-bound conjecture. There are no solvable compatible Lie extensions of $\mathcal{L}_s$ of dimension greater than $\underline{n_s}+5$.

Diagonal derivation conjecture. Every rigid real solvable Lie algebra possesses at least one diagonal derivation.

Let $\frak{r}$ be a solvable rigid Lie algebra. Its center is the subalgebra of elements that commute with every element of $\frak{r}$. Carles's trivial-center conjecture. Every so…

Cohomological lower-bound conjecture.

Let $\mathfrak{g}$ be a finite-dimensional minimal-graph-admissible Lie algebra associated with a minimal graph $G(V,E)$, and let $\mathcal{Z}(\mathfrak{g})$ denote its center. Sol…

Let $\mathcal{N}$ be a nilpotent Lie algebra that is not characteristically nilpotent, and assume that all nil-independent derivations are represented by upper-triangular matrices.…

Let $\mathfrak{n}$ be a complex nilpotent Lie algebra that is not characteristically nilpotent. Let $\mathfrak{s}$ and $\tilde{\mathfrak{s}}$ be solvable Lie algebras with nilradic…

Let $\ngo$ be a nilpotent Lie algebra, and let $\Cone$ be a cone in the maximal torus of derivations of $\ngo$. Let $\sg$ be a solvable Lie algebra with nilradical $\ngo$. The nota…

Let $\mathfrak{s}$ be a solvable Lie algebra with nilradical $\mathfrak{n}$, and let $Y\in\mathfrak{s}$. The subspace $\mathbb{R}Y\oplus\mathfrak{n}$ is the corresponding rank-one…

Let $\mathfrak{s}$ be a solvable Lie algebra with nilradical $\mathfrak{n}$. For a nilpotent Lie algebra $\mathfrak{n}$, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diag…

Let $L$ be a maximal solvable Lie algebra with nilradical $N$. A local derivation on $L$ is a linear map such that, for every $x\in L$, there exists a derivation $D_x$ of $L$ with…

Let ${\mathfrak n}$ be a complex nilpotent Lie algebra that is not characteristically nilpotent. Let ${\mathfrak s}$ and $\tilde{{\mathfrak s}}$ be solvable Lie algebras with nilra…