Question 1:Is it true that the selfinjective (finite dimensional over an algebraically closed field K) algebras $A$ such that the stable module category of $A$ is 2-Calabi-Yau are exactly the deformed preprojective algebras of generalized Dynkin type $A_n, D_n, E_n ,L_n$?
This was asked as problem 10 in the article "Periodic algebras" by Skowronski and Erdmann from 2008. I search for a reference for an up to date status of that problem.
Question 2: What is the classification of such deformed preprojective algebras of generalized Dynkin type $A_n, D_n, E_n ,L_n$ up to socle equivalence?
Are two such algebras socle equivalent to each other if they have the same Dynkin type?
