{"paper":{"title":"Isomorphisms of non noetherian down-up algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andrea Solotar, Sergio Chouhy","submitted_at":"2016-11-08T18:25:34Z","abstract_excerpt":"We solve the isomorphism problem for non noetherian down-up algebras $A(\\alpha,0,\\gamma)$ by lifting isomorphisms between some of their non commutative quotients. The quotients we consider are either quantum polynomial algebras in two variables for $\\gamma = 0$ or quantum versions of the Weyl algebra $A_1$ for non zero $\\gamma$. In particular we obtain that no other down-up algebra is isomorphic to the monomial algebra $A(0,0,0)$. We prove in the second part of the article that this is the only monomial algebra within the family of down-up algebras. Our method uses homological invariants that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02645","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"}