{"paper":{"title":"On the Hall algebra of coherent sheaves on P^1 over F_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"Matt Szczesny","submitted_at":"2010-09-18T17:09:40Z","abstract_excerpt":"We define and study the category $Coh_n(\\Pone)$ of normal coherent sheaves on the monoid scheme $\\Pone$ (equivalently, the $\\mathfrak{M}_0$-scheme $\\Pone / \\fun$ in the sense of Connes-Consani-Marcolli \\cite{CCM}). This category resembles in most ways a finitary abelian category, but is not additive. As an application, we define and study the Hall algebra of $Coh_n(\\Pone)$. We show that it is isomorphic as a Hopf algebra to the enveloping algebra of the product of a non-standard Borel in the loop algebra $L {\\mathfrak{gl}}_2$ and an abelian Lie algebra on infinitely many generators. This shoul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3570","kind":"arxiv","version":4},"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"}