Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras

Abstract

Let $\Lambda$ be an Auslander's 1-Gorenstein Artinian algebra with global dimension two. If $\Lambda$ admits a trivial maximal 1-orthogonal subcategory of $\mathrm{mod}\Lambda$, then for any indecomposable module $M\in \mathrm{mod}\Lambda$, we have that the projective dimension of $M$ is equal to one if and only if so is its injective dimension and that $M$ is injective if the projective dimension of $M$ is equal to two. In this case, we further get that $\Lambda$ is a tilted algebra.

13 pages; The main result in the original version of this paper is extended

References in corpus (2)

• Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories
• From Auslander Algebras to Tilted Algebras