{"paper":{"title":"Artin-Schelter regular algebras of dimension five with two generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"D.-M. Lu, G.-S. Zhou","submitted_at":"2013-03-06T14:00:05Z","abstract_excerpt":"We study and classify Artin-Schelter regular algebras of dimension five with two generators under an additional $\\mathbb Z^2$-grading by Hilbert driven Gr\\\"{o}bner basis computations. All the algebras we obtained are strongly noetherian, Auslander regular, and Cohen-Macaulay. One of the results provides an answer to Fl{\\o}ystad-Vatne's question in the context of $\\mathbb Z^2$-grading. Our results also achieve a connection between Lyndon words and Artin-Schelter regular algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1335","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"}