Taiwanese Journal of Mathematics

$\tau$-rigid Modules over Auslander Algebras

Xiaojin Zhang

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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.

Article information

Taiwanese J. Math., Volume 21, Number 4 (2017), 727-738.

Received: 6 April 2016
Revised: 21 June 2016
Accepted: 4 December 2016
First available in Project Euclid: 27 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16G10: Representations of Artinian rings 16E10: Homological dimension

Auslander algebra $\tau$-rigid module tilting module


Zhang, Xiaojin. $\tau$-rigid Modules over Auslander Algebras. Taiwanese J. Math. 21 (2017), no. 4, 727--738. doi:10.11650/tjm/7902. https://projecteuclid.org/euclid.twjm/1501120830

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