4 problems

Let $w$ be a word in the generators $x,x^*$, and let $w^*$ be its image under the involution exchanging $x$ and $x^*$. Consider the $*$-algebra … A word is unshrinkable if it canno…

Let $\mathcal{A}$ be a finite-dimensional $\ast$-algebra over $\mathbb{R}$, and let $H\in\mathcal{A}$ be self-adjoint, meaning $H^{\ast}=H$. Let $k\in\mathbb{N}$ be maximal among t…

Let $n\geq 1$, and let $\mathcal{C}_n$ be the left cell $2$-subcategory of projective functors for the star algebra considered in the paper. A simple transitive $2$-representation…

A simple transitive $2$-representation is a simple transitive action of the relevant $2$-subcategory of projective functors on a finitary category, and a cell $2$-representation is…