Auslander–Reiten translations in monomorphism categories

@article{Xiong2011AuslanderReitenTI,
  title={Auslander–Reiten translations in monomorphism categories},
  author={Bao-lin Xiong and P. Zhang and Yue-hui Zhang},
  journal={Forum Mathematicum},
  year={2011},
  volume={26},
  pages={863 - 912}
}
Abstract. We generalize Ringel and Schmidmeier's theory on the Auslander–Reiten translation of the submodule category 𝒮 2 (A)$\mathcal {S}_2(A)$ to the monomorphism category 𝒮 n (A)$\mathcal {S}_n(A)$ ; the category consists of all chains of (n-1)$(n-1)$ composable monomorphisms of A-modules. As in the case of n=2$n=2$ , 𝒮 n (A)$\mathcal {S}_n(A)$ has Auslander–Reiten sequences, and the Auslander–Reiten translation τ 𝒮 $\tau _{\mathcal {S}}$ of 𝒮 n (A)$\mathcal {S}_n(A)$ can be explicitly… Expand
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