5 problems

Chen–Xi's conjecture. Suppose two algebras $A$ and $B$ are derived equivalent. If $A$ is a Morita algebra and the dominant dimension of $B$ is at least two, then $B$ is also a Mori…

Let $K$ be a field, let $S_R(n,d)$ denote the Schur algebra over a commutative ring $R$, and let $V$ be its natural module. For $n,d\in\mathbb{N}$, write…

Dominant-dimension property conjecture. Every finite dimensional algebra with finite dominant dimension $n\geq 1$ has property $*$.

Dominant-dimension conjecture. The algebra $B$ has dominant dimension $n$.

Abrar's conjecture.