10 problems

Characteristic-three classification conjecture. Every simple finite-dimensional non-trivial transposed Poisson algebra over $\mathbb{F}$ is isomorphic to $\mathcal{W}_n(q)$ for som…

Let ${\mathfrak g}_{\mathbb C}$ be a reductive Lie algebra over ${\mathbb C}$ with Chevalley basis ${\mathcal B}$, let $R={\mathbb Z}[1/q\mid q$ is a bad prime for $\Phi]$, an…

Let $L=H(2n;\underline{1})^{(1)}$ be a Lie algebra of Hamiltonian type, with $n\geq3$, over a field of characteristic $2$. The Hamiltonian–special Hamiltonian conjecture. There exi…

Let $p=2$, and let $\mathfrak{g}$ be of type $E_7$ with maximal subalgebra $M_7$ and $M_7$-invariant subspace $L'_{-1}$ as in Theorem none7p2. For the Weisfeiler filtration…

Let $p=2$, and let $\mathfrak{g}$ be of type $E_8$ with maximal subalgebra $M_8$ and $M_8$-invariant subspace $L'_{-1}$ as in Theorem none8p2. For the Weisfeiler filtration…

Let $G$ be an algebraic group of type $E_8$ with Lie algebra $\mathfrak{g}=\operatorname{Lie}(G)$ over a field of characteristic $5$. Let $M$ be a maximal subalgebra of Cartan or M…

Let $G$ be an algebraic group of type $E_8$ with Lie algebra $\mathfrak{g}=\operatorname{Lie}(G)$ over an algebraically closed field of characteristic $5$. Let $M$ be a maximal sub…

Let $\mathfrak{X}(n,\underline{m})$ denote the minimal $p$-envelope of a simple Cartan-type Lie algebra $\mathsf{X}(n,\underline m)^{(2)}$, where…

Amended KSh conjecture. These constructions yield all $\mathbb{Z}$-graded simple finite dimensional examples of Lie algebras and Lie superalgebras in characteristic $p>0$, while th…

Let $p>2$, and let a finite-dimensional Lie algebra or Lie superalgebra have an indecomposable Cartan matrix normalized as in the source. A Chevalley basis uniqueness conjecture. T…