{"paper":{"title":"Exceptional sequences and Drinfeld double Hall algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Haicheng Zhang, Shiquan Ruan","submitted_at":"2016-12-29T06:38:58Z","abstract_excerpt":"Let $\\A$ be a finitary hereditary abelian category and $D(\\A)$ be its reduced Drinfeld double Hall algebra. By giving explicit formulas in $D(\\A)$ for left and right mutations, we show that the subalgebras of $D(\\A)$ generated by exceptional sequences are invariant under mutation equivalences. As an application, we obtain that if $\\A$ is the category of finite dimensional modules over a finite dimensional hereditary algebra, or the category of coherent sheaves on a weighted projective line, the double composition algebra of $\\A$ is generated by any complete exceptional sequence. Moreover, for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09051","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"}