10 problems

Property PB conjecture. All restricted Lie algebras satisfy Property PB regardless of representation type.

Property PC conjecture. For any restricted Lie algebra ${\mathfrak g}$ over $k$, ${\mathfrak g}$ satisfies Property PC if and only if ${\mathfrak g}$ is of tame or finite represent…

Let $p=2$, let $\mathcal L=\operatorname{Lie}(v_1,v_2)$ be the Fibonacci Lie algebra, and let $\mathbf L=\operatorname{Lie}_p(v_1,v_2)$ be its Fibonacci restricted version. The sou…

Let $p=2$ and let $\mathbf L=\operatorname{Lie}_p(v_1,v_2)$ be the Fibonacci restricted Lie algebra. Infinite-presentation conjecture. The algebra $\mathbf L$ is infinitely present…

Let $p=2$, let $R$ be the truncated polynomial ring from the construction, let $\mathcal L=\operatorname{Lie}(v_1,v_2)\subset\operatorname{Der}R$ be the Fibonacci Lie algebra, and…

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…

Kac–Weisfeiler conjecture (KW1).

Restricted cohomological-dimension-one structure conjecture. Any Lie $p$-algebra $L$ with $\operatorname{cd}_*(L)=1$ is of the form

Two-dimensional subalgebra conjecture. $L$ contains a two-dimensional subalgebra.

Premet's conjecture. There exists a nonempty Zariski open subset $V\subseteq{\mathfrak g}$ consisting of regular elements such that, for any $u,v\in V$, the Cartan subalgebras