{"paper":{"title":"$\\imath$Hall algebras of weighted projective lines and quantum symmetric pairs III: quasi-split type","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Ming Lu, Shiquan Ruan","submitted_at":"2024-11-20T07:07:17Z","abstract_excerpt":"From a category $\\mathcal{A}$ with an involution $\\varrho$, we introduce $\\varrho$-complexes, which are a generalization of (bounded) complexes, periodic complexes and modules of $\\imath$quiver algebras. The homological properties of the category $\\mathcal{C}_\\varrho(\\mathcal{A})$ of $\\varrho$-complexes are given to make the machinery of semi-derived Ringel-Hall algebras applicable. The $\\imath$Hall algebra of the weighted projective line $\\mathbb{X}$ is the twisted semi-derived Ringel-Hall algebra of $\\mathcal{C}_\\varrho({\\rm coh}(\\mathbb{X}))$, where $\\varrho$ is an involution of ${\\rm coh}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13078","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/2411.13078/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"}