τ-rigid modules over Auslander algebras

الأصل · EN

We give a characterization of τ-rigid modules over Auslander algebras in terms of projective dimension of modules. Moreover, we show that for an Auslander algebra Λ admitting finite number of non-isomorphic basic tilting Λ-modules and tilting Λop-modules, if all indecomposable τ-rigid Λ-modules of projective dimension 2 are of grade 2, then Λ is τ-tilting finite.