{"paper":{"title":"Point modules over the universal enveloping algebras of color Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The point modules over universal enveloping algebras of color Lie algebras are determined by a newly defined q'-Heisenberg normal element.","cross_cats":[],"primary_cat":"math.RA","authors_text":"Shu Minaki","submitted_at":"2026-04-01T03:58:42Z","abstract_excerpt":"Let $k$ be an algebraically closed field with characteristic zero. In this paper, we define the notion of a $q'$-Heisenberg normal element of a $\\mathbb{Z}$-graded $k$-algebra. This $q'$-Heisenberg normal element gives the structure of some sets of modules related to point modules. We also determine the set of point modules over an Artin--Schelter regular algebra obtained as the universal enveloping algebra of a color Lie algebra. Moreover, we give a concrete integer such that the inverse system of its truncated point schemes is constant. This is a quantitative answer to a question raised by A"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we determine the set of point modules over an Artin--Schelter regular algebra obtained as the universal enveloping algebra of a color Lie algebra. Moreover, we give a concrete integer such that the inverse system of truncated point schemes of it is constant.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The algebra obtained as the universal enveloping algebra of the color Lie algebra is Artin-Schelter regular and the newly defined q'-Heisenberg normal element behaves as required to control the point modules.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The set of point modules over the universal enveloping algebra of a color Lie algebra is determined and a concrete integer is given making the inverse system of truncated point schemes constant.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The point modules over universal enveloping algebras of color Lie algebras are determined by a newly defined q'-Heisenberg normal element.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"05a1d531a9da4fc08fe120397a0d169cc6b8be252452623eb3c28f7532bfdc18"},"source":{"id":"2604.00450","kind":"arxiv","version":3},"verdict":{"id":"84b8cd8c-fa10-45b9-9e9a-046fbd98830e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T22:37:09.835591Z","strongest_claim":"we determine the set of point modules over an Artin--Schelter regular algebra obtained as the universal enveloping algebra of a color Lie algebra. Moreover, we give a concrete integer such that the inverse system of truncated point schemes of it is constant.","one_line_summary":"The set of point modules over the universal enveloping algebra of a color Lie algebra is determined and a concrete integer is given making the inverse system of truncated point schemes constant.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The algebra obtained as the universal enveloping algebra of the color Lie algebra is Artin-Schelter regular and the newly defined q'-Heisenberg normal element behaves as required to control the point modules.","pith_extraction_headline":"The point modules over universal enveloping algebras of color Lie algebras are determined by a newly defined q'-Heisenberg normal element."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.00450/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"}