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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.5395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-24T14:56:02Z","cross_cats_sorted":["math.CO","math.CT","math.RA"],"title_canon_sha256":"d33b7669132e8612c33246c4a6bb529991b7b9f5a52537c6b64145e9a62e4fc3","abstract_canon_sha256":"54f8438eb64f86c41131745fd0fc2bd005ae4dd01b8de0b65ed0e1287891588a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:13.346360Z","signature_b64":"ll1V/eKnnMx7MUO/1eJRGTPlZj7PK+oazY3zSOPjUGwfP7M7QcGhII1I/XVHamLIZ1Kf8ezB8jk1463k3vz2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d84fa6bd7be51f30c30f57008d15911421248a2ee89311e5ad37c7689982c18d","last_reissued_at":"2026-05-18T03:57:13.345844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:13.345844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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