{"paper":{"title":"Hochschild cohomology of Beilinson algebras of graded down-up algebras with weights ($n,m$)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ayako Itaba, Shu Minaki","submitted_at":"2025-11-25T11:20:55Z","abstract_excerpt":"Let $A=A(\\alpha, \\beta)$ be a graded down-up algebra with weights $(\\mathrm{deg}\\, x, \\mathrm{deg}\\, y)=(n,m)$ and $\\beta \\neq 0$, and $\\nabla A$ its Beilinson algebra. Such an algebra $A$ is a 3-dimensional cubic AS-regular algebra by Kirkman--Musson--Passman. Assuming $\\mathrm{gcd}\\,(n, m)=1$ and $m \\geq n$, we extend the previous results on the Hochschild cohomology of $\\nabla A$. Known cases include $(n,m) = (1,1)$ (Belmans) and $(n = 1,\\,m \\geq 2)$ (Itaba--Ueyama). In this paper, we determine the dimensions of the Hochschild cohomology groups of $\\nabla A$ in the remaining case $n\\geq 2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.20195","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/2511.20195/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"}