The Existence of Maximal $n$-Orthogonal Subcategories
| dc.creator | Huang, Zhaoyong | |
| dc.creator | Zhang, Xiaojin | |
| dc.date | 2009-03-04 | |
| dc.date.accessioned | 2026-07-07T12:49:03Z | |
| dc.date.available | 2026-07-07T12:49:03Z | |
| dc.description | For 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. | |
| dc.description | 19 pages, to appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/0903.0758 | |
| dc.identifier | http://arxiv.org/abs/0903.0758 | |
| dc.identifier | doi:10.1016/j.jalgebra.2009.01.036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222268 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16G10; 16E10 | |
| dc.title | The Existence of Maximal $n$-Orthogonal Subcategories | |
| dc.type | text |