15 problems

Deré's conjecture. If $L$ is isomorphic to its complex conjugate, then $L$ is defined over $\mathbb{R}$; equivalently, there exists a real Lie algebra $L_{\mathbb{R}}$ such that

Let $\mathfrak{g}$ be a finite-dimensional nilpotent Lie algebra over $\mathbb{k}$, and set $A=\operatorname{CE}(\mathfrak{g})$. Let $S$ be the symmetric algebra governing the Kosz…

Let $\mathfrak{g}$ be a finite-dimensional $k$-step nilpotent Lie algebra. Nilpotent minimal-graph-admissibility conjecture. If $k\leq 2$, then $\mathfrak{g}$ is minimal-graph-admi…

Let $(\mathfrak{g}, \{J_{\alpha}\})$ be a nilpotent hypercomplex Lie algebra. Here, $\mathbb{H}$-solvability means that the descending $\mathbb{H}$-central series defined by…

Let $n$ and $p$ be integers with $n<p$, and let $L$ be an $n$-Engel Lie algebra over $\mathbb{F}_p$. For every $x e L$, let $I(x)$ be the ideal generated by $x$; call $L$ **$k$-str…

Let $0\ne a\in\mathbf L$ be written in the basis as $a=\sum_{j=n}^{m}r_{j-3}v_j$, with $r_j\in R$. The preceding result gives the bound $a^{2^{m-n+2}}=0$. Optimality conjecture. Th…

Let $L$ be a finite-dimensional nilpotent Lie algebra defined over the rational numbers, and let $C(L)$ denote its center. Nilpotent Lie algebra toral rank conjecture. Then … This…

Let $\mathfrak{n}$ be a nilpotent Lie algebra, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diagonalizable derivations, let $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$ be…

Let $\mathfrak{n}$ be a nilpotent Lie algebra, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diagonalizable derivations, and let…

Let $\mathfrak{n}$ be a nilpotent Lie algebra and let $\operatorname{Der}(\mathfrak{n})_{\mathrm{rn}}$ denote the derivations whose associated solvable extension admits a Ricci-neg…

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 $\mathfrak{g}$ be a nilpotent Lie algebra over a field $\mathbb{F}$. For an element $x\in\mathfrak{g}$, define its breadth $b(x)$ by … where $C_{\mathfrak{g}}(x)$ is the Lie ce…

Let $G$ be a semisimple Lie group with a $\Theta$-positive structure, with nilpotent Lie algebra $\mathfrak{u}_\Theta$ and positivity cones $c^\circ_\beta$ for $\beta\in\Theta$. Th…

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…