6 problems

Wan's conjecture. For $a\in\mathbb F_q^{\times}$, regular $x\in B^{\times}$, and integer $r\ge2$, one has

Let $B$ be a semisimple algebra of dimension $n$ over $\q$. For $a\in \q^*$, let $x\in B^*$ be regular and let $r\geq 2$ be an integer. Writing … so that…

Let $K$ be an algebraically closed field of characteristic zero, let $\alpha_1,\alpha_2\in K$, and let $\mathcal{D}_4(\alpha_1,\alpha_2)$ be the quadratic $K$-algebra generated by…

Let $A$ be a finite-dimensional semisimple complex algebra of the form specified in the source, with multiplicities $b(n)$ in its decomposition. A connected grading of $A$ is compl…

Let $H$ be a semisimple Hopf algebra, and let $\operatorname{Irr} {}_{H}^{}\mathcal{M}$ denote the set of isomorphism classes of irreducible finite-dimensional $H$-modules. Kaplans…

Semisimplicity conjecture. The CGW algebra is semisimple except possibly if $r$ is a root of unity or if