12 problems

Characteristic-extension conjecture. Theorem 0.2 also holds when

Let $B$ be a local commutative algebra over $k$ with maximal ideal ${\mathfrak m} \subset B$, and let $\widetilde{A}$ be a flat associative algebra over $B$ such that…

Adjamagbo's separable Jacobian conjecture. Assume that

Kostrikin–Šafarevič conjecture. $L$ is of classical or Cartan type.

Positive-answer conjecture. The question introduced in the source is conjectured to have a positive answer.

Let $k_p$ be the ground field of characteristic $p$, with $p\geq 7$, and let $\mathfrak{g}$ be a finite-dimensional simple Lie superalgebra over $k_p$. The examples of Proposition…

Classification conjecture. If $L$ admits a nontrivial Hom-Lie structure, then $L$ is isomorphic either to a $3$-dimensional simple algebra, or, in the case of positive characterist…

Let $k$ be a field of characteristic $p>0$, and consider the class of restricted Lie algebras, including the classical restricted Lie algebras and the four algebras arising in Cart…

Let $p>3$ be the characteristic, let ${\boldsymbol{k}}$ be the base field, and let $g,x,y$ be generators with parameters $\epsilon\in\{0,1\}$ and $\mu,\tau\in{\boldsymbol{k}}$. Let…

Let $k$ be an algebraically closed field of characteristic $p>0$, and let $K$ be a semisimple Hopf algebra that is not necessarily cosemisimple. Consider the conclusions of Theorem…

Let $p>0$ be the characteristic of a field ${\bf k}$, let $K={\bf k}[y_1,y_2,y_3\mid y_i^p=0,\ i=1,2,3]$, and let … Let $\Lambda_p$ denote the Jacobson-Zassenhaus Lie polynomial, s…

Let $H_c$ be the infinitesimal Cherednik algebra associated with $\mathfrak{g}=\mathfrak{gl}_n$ and parameter $c$ over a field of characteristic $p$, equipped with its standard fil…