Auslander-Reiten Translations in Monomorphism Categories

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Applying the above theorem to the selfinjective Nakayama algebras A(m, t), we get Corollary 4.2 Let FS be the Serre functor of Sn(A(m, t)) with m ≥ 1, t ≥ 2, and X be an arbitrary object in Sn(A(m, t)). Then (i) If t = 2, then F N(n+1) S X ∼ = X, where N = m (m,n−1) . (ii) If t ≥ 3, then F N(n+1) S X ∼ = X, where N = m (m,t,n+1) . Bao-Lin Xiong (SJTU) Auslander-Reiten Translations in Monomorphism Categories ISPN ’80 23 / 24
Thank you! E-mail: xiongbaolin@gmail.com Bao-Lin Xiong (SJTU) Auslander-Reiten Translations in Monomorphism Categories ISPN ’80 24 / 24
Page 1 and 2: Auslander-Reiten Translations in Mo
Page 3 and 4: Motivation C. M. Ringel and M. Schm
Page 5 and 6: The notions A: an Artin algebra, A-
Page 7 and 8: The notions The monomorphism catego
Page 9 and 10: The kernel and cokernel functors Ke
Page 11 and 12: The functor: Mono Mono : Morn(A)
Page 13 and 14: The object MimoX (φi) Define MimoX
Page 15 and 16: Remark 2.2 The process means: Give
Page 17 and 18: An example The Auslander-Reiten qui
Page 19 and 20: Applications to selfinjective algeb
Page 21 and 22: The rotation of X (φi) The rotatio
Page 23 and 24: For X (φi ) ∈ Morn(A-mod), defin
Page 25 and 26: Theorem 3.3 Let A be a selfinjectiv
Page 27 and 28: An example Let X (φi ) be an indec
Page 29: Theorem 4.1 Let A be a selfinjectiv

Auslander-Reiten Translations in Monomorphism Categories

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