5 problems

Let $d\in\mathbb{N}$ and let ${\bf q}\in\mathbb{C}^{\{1,2\}^d}$ be a $d$-dimensional tensor defining a Weyl groupoid through the generalized Rosso condition. Rank-two realization c…

Let $d$ be an even tensor power and let the generalized Rosso condition associate a Weyl groupoid to a higher diagonal braiding. Asymptotic realization conjecture. Every finite Wey…

Let $C_n$ be the cyclic group of order $n$, and let $\mathcal{B}_{C_n}$ denote the Nichols algebra with the braiding considered in the paper. Weyl-groupoid conjecture. The Weyl gro…

Let $C_n$ be the cyclic group of order $n$, and let $\mathcal{B}(Y_{C_n})$ be the Nichols algebra associated with the cyclic-group construction. Its associated Weyl groupoid is the…

Affine Weyl groupoid conjecture. The finite Weyl groupoids occurring as parabolic subgroupoids in affine Weyl groupoids of rank three are exactly the arithmetic root systems of ran…