Abstract
We give a characterization of $\tau$-rigid modules over Auslander algebras in terms of projective dimension of modules. Moreover, we show that for an Auslander algebra $\Lambda$ admitting finite number of non-isomorphic basic tilting $\Lambda$-modules and tilting $\Lambda^{\operatorname{op}}$-modules, if all indecomposable $\tau$-rigid $\Lambda$-modules of projective dimension $2$ are of grade $2$, then $\Lambda$ is $\tau$-tilting finite.
Citation
Xiaojin Zhang. "$\tau$-rigid Modules over Auslander Algebras." Taiwanese J. Math. 21 (4) 727 - 738, 2017. https://doi.org/10.11650/tjm/7902
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