2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222268For an $(n-1)$-Auslander algebra $Λ$ with global dimension $n$, we give some necessary conditions for $Λ$ admitting a maximal $(n-1)$-orthogonal subcategory in terms of the properties of simple $Λ$-modules with projective dimension $n-1$ or $n$. For an almost hereditary algebra $Λ$ with global dimension 2, we prove that $Λ$ admits a maximal 1-orthogonal subcategory if and only if for any non-projective indecomposable $Λ$-module $M$, $M$ is injective is equivalent to that the reduced grade of $M$ is equal to 2. We give a connection between the Gorenstein Symmetric Conjecture and the existence of maximal $n$-orthogonal subcategories of $^{\bot}T$ for a cotilting module $T$. For a Gorenstein algebra, we prove that all non-projective direct summands of a maximal $n$-orthogonal module are $Ω^nτ$-periodic. In addition, we study the relation between the complexity of modules and the existence of maximal $n$-orthogonal subcategories for the tensor product of two finite-dimensional algebras.19 pages, to appear in Journal of AlgebraRepresentation TheoryRings and Algebras16G10; 16E10text