M ar 2 00 9 From Auslander Algebras to Tilted Algebras
نویسندگان
چکیده
For an (n − 1)-Auslander algebra Λ with global dimension n ≥ 2, we show that if Λ admits a trivial maximal (n − 1)-orthogonal subcategory of modΛ, then Λ is of finite representation type and the projective dimension or injective dimension of any indecomposable module in modΛ is at most n − 1. As a result, we have that for an Auslander algebra Λ with global dimension 2, if Λ admits a trivial maximal 1-orthogonal subcategory of modΛ, then Λ is a tilted algebra of finite representation type; furthermore, in case there exists a unique simple module in modΛ with projective dimension 2, then the converse also holds true.
منابع مشابه
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