{"paper":{"title":"Cotorsion pairs and t-structures in a $2-$Calabi-Yau triangulated category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Bin Zhu, Yu Zhou","submitted_at":"2012-10-24T02:53:07Z","abstract_excerpt":"For a Calabi-Yau triangulated category $\\mathcal{C}$ of Calabi-Yau dimension $d$ with a $d-$cluster tilting subcategory $\\mathcal{T}$, it is proved that the decomposition of $\\mathcal{C}$ is determined by the special decomposition of $\\mathcal{T}$, namely, $\\mathcal{C}=\\oplus_{i\\in I}\\mathcal{C}_i$, where $\\mathcal{C}_i, i\\in I$ are triangulated subcategories, if and only if $\\mathcal{T}=\\oplus_{i\\in I}\\mathcal{T}_i,$ where $\\mathcal{T}_i, i\\in I$ are subcategories with $Hom_{\\mathcal{C}}(\\mathcal{T}_i[t],\\mathcal{T}_j)=0, \\forall 1\\leq t\\leq d-2$ and $i\\not= j.$ This induces that the Gabriel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6424","kind":"arxiv","version":2},"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"}