{"paper":{"title":"Induced and Coinduced Modules in Cluster-Tilted Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Khrystyna Serhiyenko, Ralf Schiffler","submitted_at":"2014-10-07T14:00:58Z","abstract_excerpt":"We propose a new approach to study the relation between the module categories of a tilted algebra $C$ and the corresponding cluster-tilted algebra $B=C\\ltimes E$. This new approach consists of using the induction functor $-\\otimes_C B$ as well as the coinduction functor $D(B\\otimes_C D-)$. We show that $DE$ is a partial tilting and a $\\tau$-rigid $C$-module and that the induced module $DE\\otimes_C B$ is a partial tilting and a $\\tau$-rigid $B$-module. Furthermore, if $C=\\text{End}_A T$ for a tilting module $T$ over a hereditary algebra $A$, we compare the induction and coinduction functors to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1732","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"}