Higher Auslander algebras admitting trivial maximal orthogonal subcategories

In this paper, we prove that Λ is an (n−1)-Auslander Artinian algebra with admitting a trivial maximal (n−1)-orthogonal subcategory of mod Λ if and only if it is Morita equivalent to a finite product of F and , where F is a division algebra. In addition, we obtain a necessary condition for an Auslander Artinian algebra admitting a non-trivial maximal 1-orthogonal subcategory.