{"paper":{"title":"Auslander-Reiten translations in monomorphism categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bao-Lin Xiong, Pu Zhang, Yue-Hui Zhang","submitted_at":"2011-01-21T11:31:48Z","abstract_excerpt":"We generalize Ringel and Schmidmeier's theory on the Auslander-Reiten translation of the submodule category $\\mathcal S_2(A)$ to the monomorphism category $\\mathcal S_n(A)$. As in the case of $n=2$, $\\mathcal S_n(A)$ has Auslander-Reiten sequences, and the Auslander-Reiten translation $\\tau_{\\mathcal{S}}$ of $\\mathcal S_n(A)$ can be explicitly formulated via $\\tau$ of $A$-mod. Furthermore, if $A$ is a selfinjective algebra, we study the periodicity of $\\tau_{\\mathcal{S}}$ on the objects of $\\mathcal S_n(A)$, and of the Serre functor $F_{\\mathcal S}$ on the objects of the stable monomorphism ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4113","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}