{"paper":{"title":"Mutation graphs of maximal rigid modules over finite dimensional preprojective algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hongbo Yin, Shunhua Zhang","submitted_at":"2013-01-17T05:04:35Z","abstract_excerpt":"Let $Q$ be a finite quiver of Dynkin type and $\\Lambda=\\Lambda_Q$ be the preprojective algebra of $Q$ over an algebraically closed field $k$. Let $\\mathcal {T}_\\Lambda$ be the mutation graph of maximal rigid $\\Lambda$ modules. Geiss, Leclerc and Schr$\\ddot{\\rm o}$er conjectured that $\\mathcal {T}_\\Lambda$ is connected, see [C.Geiss, B.Leclerc, J.Schr\\\"{o}er, Rigid modules over preprojective algebras, Invent.Math., 165(2006), 589-632]. In this paper, we prove that this conjecture is true when $\\Lambda$ is of representation finite type or tame type. Moreover, we also prove that $\\mathcal {T}_\\La"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3983","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"}