{"paper":{"title":"Simple modules over the 4-dimensional Sklyanin Algebras at points of finite order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"S. Paul Smith","submitted_at":"2018-02-16T16:48:19Z","abstract_excerpt":"In 1982 E.K. Sklyanin defined a family of graded algebras $A(E,\\tau)$, depending on an elliptic curve $E$ and a point $\\tau \\in E$ that is not 4-torsion. The present paper is concerned with the structure of $A$ when $\\tau$ is a point of finite order, $n$ say. It is proved that every simple $A$-module has dimension $\\le n$ and that \"almost all\" have dimension precisely $n$. There are enough finite dimensional simple modules to separate elements of $A$; that is, if $0\\ne a \\in A$, then there exists a simple module $S$ such that $a.S \\ne 0.$ Consequently $A$ satisfies a polynomial identity of deg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06023","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"}