4 problems

For each $m\in\mathbb{N}$, let $\chi_m$ denote the algebra map defined in the paper. Chi-map isomorphism conjecture. The map $\chi_m$ is an isomorphism of algebras for all…

Let $B$ be the graded algebra under consideration, let $B_\psi=B/\langle b-\psi(b)\mid b\in B\rangle$, and let $C$ be the graded vector space with basis $v_d$ for…

Let $I$ be the vertex set of the Dynkin diagram. For $i\in I$ and $k\in\mathbb{N}$, let $c_k^i$ be a clockwise circle labeled $i$ containing exactly $k$ hollow dots, and let $c_k$…

Injectivity conjecture. The natural map is injective. This conjecture identifies the explicitly presented algebra $H_i^n$ with a subalgebra of the endomorphism algebra; the source…