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arXiv · 1608.08723

τ-rigid modules over Auslander algebras

Xiaojin Zhang
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Abstract

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 $Λ^{op}$-modules, if all indecomposable $τ$-rigid $Λ$-modules of projective dimension $2$ are of grade $2$, then $Λ$ is $τ$-tilting finite.

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Xiaojin Zhang. 2017-02-26. τ-rigid modules over Auslander algebras. https://doi.org/10.11650/tjm.xx.20xx.7902

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