Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
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Motivation<br />
C. M. R<strong>in</strong>gel and M. Schmidmeier, 2008:<br />
1 The submodule category S(A) of an Art<strong>in</strong> algebra A has<br />
AR-sequences.<br />
2 τSX ∼ = Mimo τ CokX for X ∈ S(A), where τS (resp. τ) is the<br />
AR-translation <strong>in</strong> S(A) (resp. A-mod).<br />
3 If A is commutative uniserial then τ 6 S X ∼ = X for each<br />
<strong>in</strong>decomposable nonprojective object X ∈ S(A).<br />
Question: Can we generalize the above theory?<br />
Bao-L<strong>in</strong> Xiong (SJTU) <strong>Auslander</strong>-<strong>Reiten</strong> <strong>Translations</strong> <strong>in</strong> <strong>Monomorphism</strong> <strong>Categories</strong> ISPN ’80 2 / 24
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