9 problems

Period-four conjecture. Every tame symmetric periodic algebra of non-polynomial growth has period $4$.

Let $A$ be an indecomposable symmetric periodic tame algebra. Call its representation growth non-polynomial when it is not of polynomial growth, and let the period of $A$ be its pe…

Let $\Lambda$ be a periodic algebra, and let $\mu_\bullet(\Lambda)$ denote its mutation class, consisting of the isoclasses of algebras obtained from $\Lambda$ by finite sequences…

A finite-dimensional algebra is twisted periodic when it is isomorphic, as a bimodule, to one of its syzygies after twisting the bimodule structure by an automorphism on one side;…

Stability conjecture. For $n\geqslant 7$, the picture becomes more stable, and known examples of families of exceptional algebras appear only for $n=6$.

A finite-dimensional algebra is periodic if it is periodic as a bimodule, and it is tame and symmetric in the usual representation-theoretic senses. Its period is the least positiv…

Skowroński's conjecture. The class of weighted generalized triangulation algebras is closed under mutations and exhausts all algebras derived equivalent to weighted triangulation a…

Skowroński's conjecture. The period of $A$ is equal to four.

Let $K$ be a field of characteristic different from $2$, and let $\Delta$ be a generalized Dynkin type. Consider a deformed preprojective $K$-algebra of type $\Delta$ and the prepr…