{"paper":{"title":"Hall algebras and quantum symmetric pairs I: foundations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ming Lu, Weiqiang Wang","submitted_at":"2019-01-31T16:06:42Z","abstract_excerpt":"A quantum symmetric pair consists of a quantum group $\\mathbf U$ and its coideal subalgebra ${\\mathbf U}^{\\imath}_{\\boldsymbol{\\varsigma}}$ with parameters $\\boldsymbol{\\varsigma}$ (called an $\\imath$quantum group). We initiate a Hall algebra approach for the categorification of $\\imath$quantum groups. A universal $\\imath$quantum group $\\widetilde{\\mathbf U}^{\\imath}$ is introduced and ${\\mathbf U}^{\\imath}_{\\boldsymbol{\\varsigma}}$ is recovered by a central reduction of $\\widetilde{\\mathbf U}^{\\imath}$. The semi-derived Ringel-Hall algebras of the first author and Peng, which are closely rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11446","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.11446/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"}