{"paper":{"title":"Elliptic R-matrices and Feigin and Odesskii's elliptic algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Alex Chirvasitu, Ryo Kanda, S. Paul Smith","submitted_at":"2020-06-22T14:10:40Z","abstract_excerpt":"The algebras $Q_{n,k}(E,\\tau)$ introduced by Feigin and Odesskii as generalizations of the 4-dimensional Sklyanin algebras form a family of quadratic algebras parametrized by coprime integers $n>k\\ge 1$, a complex elliptic curve $E$, and a point $\\tau\\in E$. The main result in this paper is that $Q_{n,k}(E,\\tau)$ has the same Hilbert series as the polynomial ring on $n$ variables when $\\tau$ is not a torsion point. We also show that $Q_{n,k}(E,\\tau)$ is a Koszul algebra, hence of global dimension $n$ when $\\tau$ is not a torsion point, and, for all but countably many $\\tau$, it is Artin-Schelt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12283","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.12283/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"}