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

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

2009-03-04

arxiv.org/abs/0903.0762v2

Mathematics

Representation Theory

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

Scientific paper

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

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