{"paper":{"title":"Derived equivalences in n-angulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yiping Chen","submitted_at":"2011-07-15T03:06:29Z","abstract_excerpt":"In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient algebras of $n$-perforated Yoneda algebras. This result generalizes some results of Hu, K\\\"{o}nig and Xi. And it also establishes a connection between higher cluster theory and derived equivalences. Namely, in a cluster tilting subcategory of a triangulated category, an Auslander-Reiten $n$-angle implies a derived equivalence between two quotient algebras. This result can be compared with the fact that an Ausla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2985","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"}