{"paper":{"title":"Tilting modules and support $\\tau$-tilting modules over preprojective algebras associated with symmetrizable Cartan matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Changjian Fu, Shengfei Geng","submitted_at":"2016-12-18T08:19:46Z","abstract_excerpt":"For any given symmetrizable Cartan matrix $C$ with a symmetrizer $D$, Gei\\ss~ et al. (2016) introduced a generalized preprojective algebra $\\Pi(C, D)$. We study tilting modules and support $\\tau$-tilting modules for the generalized preprojective algebra $\\Pi(C, D)$ and show that there is a bijection between the set of all cofinite tilting ideals of $\\Pi(C,D)$ and the corresponding Weyl group $W(C)$ provided that $C$ has no component of Dynkin type. When $C$ is of Dynkin type, we also establish a bijection between the set of all basic support $\\tau$-tilting $\\Pi(C,D)$-modules and the correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05867","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"}