{"paper":{"title":"On the Hall algebra of semigroup representations over F_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Matt Szczesny","submitted_at":"2012-04-24T14:56:02Z","abstract_excerpt":"Let $\\A$ be a finitely generated semigroup with 0. An $\\A$-module over $\\fun$ (also called an $\\A$--set), is a pointed set $(M,*)$ together with an action of $\\A$. We define and study the Hall algebra $\\H_{\\A}$ of the category $\\C_{\\A}$ of finite $\\A$--modules. $\\H_{\\A}$ is shown to be the universal enveloping algebra of a Lie algebra $\\n_{\\A}$, called the \\emph{Hall Lie algebra} of $\\C_{\\A}$. In the case of the $\\fm$ - the free monoid on one generator $\\fm$, the Hall algebra (or more precisely the Hall algebra of the subcategory of nilpotent $\\fm$-modules) is isomorphic to Kreimer's Hopf alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5395","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"}