6 problems

Let $d$ be a positive integer and let $\Lambda$ be a $d$-representation-finite $\mathbb{K}$-algebra. The source refers to an acyclic property for such algebras, but does not specif…

Let $\Lambda$ be an $n$-representation infinite algebra. Write $\mathscr{R}$ for its category of $n$-regular modules, and let $\mathsf{D}^{\rm b}(\operatorname{mod}\Lambda)$ be the…

Let $\Lambda$ be an $n$-hereditary algebra. Its representation dimension $\operatorname{repdim}\Lambda$ measures the homological complexity of $\Lambda$ through the global dimensio…

Let $\Lambda$ be an $n$-representation infinite algebra, and let $\mathscr{R}$ denote its category of $n$-regular modules. Nonvanishing conjecture. The category $\mathscr{R}$ is no…

Let $n\ge2$, let $\Lambda$ be in the setting of the paper, and let $\mathscr{R}$ denote the category of $n$-regular modules inside $\mathscr{C}^{0}$. A sink morphism is a right alm…

Let $\Lambda$ be an $n$-representation infinite algebra. The representation dimension $\operatorname{repdim}\Lambda$ is the least integer $d$ such that there is an appropriate gene…