# Quasi-hereditary algebras with high dominant dimension

Note that the global dimension of a quasi-hereditary algebra with n simples is bounded by 2n-2. Two questions:

1.What are examples of quasi-hereditary algebras having n simple modules and dominant dimension 2n-2 ? Note that this implies that the algebra is in fact a higher auslander algebra. The only examples I know are the blocks of finite representation type of Schur algebras. Maybe there are no others?

2.What are examples of quasi-hereditary algebras having n simple modules and global dimension 2n-2 ? There should be many examples and maybe they can be classified?