{"paper":{"title":"Mutation graph of support $\\tau$-tilting modules over a skew-gentle algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.RA"],"primary_cat":"math.RT","authors_text":"Bin Zhu, Ping He, Yu Zhou","submitted_at":"2022-12-21T09:46:35Z","abstract_excerpt":"Let $\\mathcal{D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object $R$. Let $\\Lambda=\\operatorname{End}_{\\mathcal{D}}R$ be the endomorphism algebra of $R$. We introduce the notion of mutation of maximal rigid objects in the two-term subcategory $R\\ast R[1]$ via exchange triangles, which is shown to be compatible with mutation of support $\\tau$-tilting $\\Lambda$-modules. In the case that $\\mathcal{D}$ is the cluster category arising from a punctured marked surface, it is shown that the graph of mutations of support $\\tau$-tilting $\\Lambda$-modules is isomor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.10880","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.10880/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}