5 problems

Let $A$ be a finite-dimensional $K$-algebra over an algebraically closed field $K$. Say that $A$ has a well-defined Auslander–Reiten map if every indecomposable injective $A$-modul…

Let $A$ be a finite-dimensional algebra over a field. An Auslander-Reiten sequence is called $n$-torsion-free when it has the torsion-freeness property of order $n$ considered in t…

First-level Auslander–Reiten conjecture. The module $\tau M$ is also of the first level.

The authors' conjecture. The connected components of \text{mathitGamma}_{{\rm rep}(Q)} containing representations not in $\overline{\mystrut(5,0) {\rm rep\hspace{-1pt}}}\,(Q)$…

Let $A$ be a simply connected Gorenstein differential graded algebra of finite type. Write $\operatorname{H}^eA$ and $\operatorname{H}^*A$ for its cohomology in degree $e$ and in a…