4 problems

Let $d\geq 1$, let $1\leq n\leq d$, and let $I_{n,d}$ be the set of strictly increasing $n$-tuples $(i_1,\ldots,i_n)$ with $0\leq i_1<\cdots<i_n<d$. Set $\xi=\exp(i\pi/d)$,…

Cuntz's conjecture. This multiplication is associative.

Fusion-algebra version of Wall's conjecture. The number of maximal fusion subalgebras generated by a subset of the simple objects of ${\cal F}$ is less than $n$.

Conjectural radical presentation. For $\mathfrak{g}$ of type $B_r$ with $r\geq 3$,