Algebras are always finite dimensional over a field $K$. Let $X_n$ be the set of representation-finite algebras over $K$ with $n$ simple modules.
Define $g(X_n):= sup \{ gldim(A) | A \in X_n $ and $A$ has finite global dimension $\}$
and
$d(X_n):= sup \{ domdim(A) | A \in X_n $ and $A$ has finite dominant dimension $\}$.
Questions: What can be said about those sequences? My guess is that those sequences are equal to $2n-2$ and the maximum is attained (uniquely up to derived equivalence?) at the representation-finite block of a Schur algebra. Is there a good proof that those numbers are finite (what I expect). Are there good bounds?
