9 problems

Hanlon–Wales semisimplicity conjecture. The algebra $\mathfrak{B}_n(\delta)$ is always semisimple if $\delta \in \mathbb{C}$ is not an integer.

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…

Gelaki–Westreich's conjecture. Any semisimple Hopf algebra of dimension $pq$ over $k$ is either a group algebra or the dual of a group algebra.

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

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 $k$ be the field under consideration, and for each positive integer $n$ let $\operatorname{gap}(n)$ be the first integer that is not the dimension of a semisimple subalgebra of…

Let $A$ be a semisimple finite-dimensional associative algebra over a field $F$ of characteristic zero, decomposed as … where each $A_i$ is simple. Write $\operatorname{rb}(A)$ for…

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…

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