{"paper":{"title":"A proof of extension conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.RT","authors_text":"Yang Han","submitted_at":"2013-09-02T05:19:33Z","abstract_excerpt":"Extension conjecture states that if a simple module over an artin algebra has nonzero first self-extension group then it has nonzero i-th self-extension group for infinitely many positive integers i. It is shown by recollement of triangulated categories and differential graded homological algebra approach that extension conjecture is true for finite-dimensional elementary algebras over a field, particularly, for finite-dimensional algebras over an algebraically closed field. Moreover, bimodule approach is introduced to strong no loop conjecture, which provides two new proofs of Igusa-Liu-Paque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0304","kind":"arxiv","version":4},"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"}