{"paper":{"title":"Decorated marked surfaces III: The derived category of a decorated marked surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Aslak Bakke Buan, Yu Qiu, Yu Zhou","submitted_at":"2018-03-31T00:40:00Z","abstract_excerpt":"We study the Ginzburg dg algebra $\\Gamma_\\mathbf{T}$ associated to the quiver with potential arising from a triangulation $\\mathbf{T}$ of a decorated marked surface $\\mathbf{S}_\\bigtriangleup$, in the sense of Qiu. We show that there is a canonical way to identify all finite dimensional derived categories $\\mathcal{D}_{fd}(\\Gamma_\\mathbf{T})$, denoted by $\\mathcal{D}_{fd}(\\mathbf{S}_\\bigtriangleup)$. As an application, we show that the spherical twist group $\\operatorname{ST}(\\mathbf{S}_\\bigtriangleup)$ associated to $\\mathcal{D}_{fd}(\\mathbf{S}_\\bigtriangleup)$ acts faithfully on its space of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00094","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"}