M ar 2 00 9 From Auslander Algebras to Tilted Algebras

Abstract

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.

Cite this paper

@inproceedings{Huang2009MA2, title={M ar 2 00 9 From Auslander Algebras to Tilted Algebras}, author={Zhaoyong Huang and Xiaojin Zhang}, year={2009} }