31 problems

Let $G$ be a reductive algebraic group with Lie algebra ${\mathfrak g}$ over a field of characteristic $p$, let $\chi\in{\mathfrak g}^{*}$, and let $U_\chi({\mathfrak g})$ be the r…

Let $\mathfrak g'$ be the Lie algebra of a semisimple algebraic group $G'$ over an algebraically closed field $\mathbf{k}$ of characteristic $p>0$. For a linear form $\theta$ on…

Let $\Kee$ be an algebraically closed field of characteristic $p>7$, and consider simple finite-dimensional restricted Lie algebras over $\Kee$. Kostrikin–Shafarevich conjecture. T…

Let $\mathfrak{g}$ be a finite-dimensional Lie algebra over a field $\mathbb{F}$. Write $\operatorname{Der}(\mathfrak{g})$ for its derivation algebra, let…

Let $\mathbb K$ be an algebraically closed field of characteristic $p>0$. For a simple finite-dimensional complex Lie algebra $\mathfrak g$, let $\mathfrak g_{\mathbb Z}$ be a…

Let $p>3$, and consider finite dimensional simple Lie algebras arising from the Hamiltonian forms discussed in the source. Kostrikin's nonexistence conjecture. No multiparameter fa…

Let $F$ be a field of characteristic $p>5$. A finite dimensional Lie algebra over $F$ is restrictable when its adjoint representation admits the relevant restricted structure. The…

Let $F$ be a field of characteristic $p>3$. A Lie algebra $L$ over $F$ is almost classical if there is a direct sum $\mathfrak g$ of classical simple Lie algebras such that … Let…

Let $F$ be a field of characteristic $p>5$, let $L$ be a strongly degenerate simple Lie algebra over $F$, and let ${\mathcal S}(L)=\{s\in L\mid (\operatorname{ad}s)^2=0\}$. Write…

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 $R={\mathbb Z}[1/q\mid q\text{ is a bad prime for }\Phi]$, an…

Let $\fg$ be a simple W-graded infinite-dimensional vectorial Lie superalgebra over a field of characteristic $p=2$ or $3$. The proposed construction method searches for irreducibl…

Let $\mathcal{L}$ be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic $p>3$. An element $c\in\mathcal{L}$ is a sandwich element if…

Let $L$ be a modular simple Lie algebra of classical type over an algebraically closed field $F$ of characteristic $p\geq 7$, with rank $\operatorname{rank}(L)$ and dimension…

Let $L$ be a modular simple Lie algebra of classical type over an algebraically closed field $F$ of characteristic $p\geq 7$. Let $V_\chi^\lambda(L)$ and $W_\chi^\lambda(L)$ denote…

YangGon's dimension conjecture. Any simple $L$-module with character $\chi$ has dimension

We consider modular Lie algebras over an algebraically closed field of characteristic $p\geq 7$. A Park's Lie algebra is a modular Lie algebra of the type considered in the source,…

Let $K$ be a field, let $\mathfrak{g}$ be a Lie algebra over $K$, and write $\operatorname{Der}(\mathfrak{g})$ and $\operatorname{Inn}(\mathfrak{g})$ for its derivation and inner d…

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…

Depth-one conjecture. A non-restricted $L_0'$-module $L_{-1}$ can exist only when the Lie algebra $L$ has depth one, that is, when $q=1$.

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…