Another construction is the preprojective algebra of a Dynkin quiver (a quiver such that the underlying graph is Dynkin).

Such an algebra is Frobenius but not in general symmetric, see for instance Erdmann, Karin; Snashall, Nicole, On Hochschild cohomology of preprojective algebras. I.

Another construction is the preprojective algebra of a Dynkin quiver (a quiver such that the underlying graph is Dynkin).

Such an algebra is Frobenius but not in general symmetric, see for instance Erdmann, Karin; Snashall, Nicole, On Hochschild cohomology of preprojective algebras. I.

Another construction is the preprojective algebra of a Dynkin quiver (a quiver such that the underlying graph is Dynkin).

Such an algebra is Frobenius but not in general symmetric.

Another construction is the preprojective algebra of a Dynkin quiver (a quiver such that the underlying graph is Dynkin).

Such an algebra is Frobenius but not in general symmetric, see for instance Erdmann, Karin; Snashall, Nicole, On Hochschild cohomology of preprojective algebras. I.