5 problems

Representation-dimension conjecture. The representation dimension of $A$ is at most three.

Let $A$ be an algebra and let $e\in A$ be an idempotent element. The representation dimension of $eAe$ is at most the representation dimension of $A$. Idempotent representation-dim…

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. The representation dimension $\operatorname{repdim}\Lambda$ is the least integer $d$ such that there is an appropriate gene…

Tame representation-dimension conjecture. The representation dimension of an algebra of tame representation type is at most three.