{"paper":{"title":"On monomial algebras with representation-finite enveloping algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chao Zhang, Jianguo Zhou, Yu-Zhe Liu","submitted_at":"2024-04-25T11:27:26Z","abstract_excerpt":"The present paper mainly considers the representation type of the enveloping algebra of monomial algebra. Let $A$ be a monomial algebra and $A^e= A\\otimes_{\\mathrm{l}\\!\\mathrm{k}} A^{\\mathrm{op}}$ its enveloping algebra. It is shown that $A^e$ is representation-finite if and only if $A \\cong \\pmb{A}_n/\\mathrm{rad}^2 \\pmb{A}_n$, where $\\pmb{A}_n$ is the path algebra $\\mathrm{l}\\!\\mathrm{k}\\mathcal{Q}$ with $\\mathcal{Q} = 1 \\longrightarrow 2 \\longrightarrow \\cdots \\longrightarrow n$. Moreover, we show that the number of all isoclasses of indecomposable $(\\pmb{A}_n/ \\mathrm{rad}^2\\pmb{A}_n)^e$-mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16521","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/2404.16521/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"}