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arXiv · 0903.0762

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

Zhaoyong Huang·Xiaojin Zhang
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Abstract

Let $Λ$ be an Auslander's 1-Gorenstein Artinian algebra with global dimension two. If $Λ$ admits a trivial maximal 1-orthogonal subcategory of $\modΛ$, then for any indecomposable module $M \in \mod Λ$, 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 $Λ$ is a tilted algebra.

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BibTeXRIS

Zhaoyong Huang, Xiaojin Zhang. 2009-06-21. Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras. https://arxiv.org/abs/0903.0762

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