{"paper":{"title":"A Parametric Family of Subalgebras of the Weyl Algebra I. Structure and Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Georgia Benkart, Matthew Ondrus, Samuel A. Lopes","submitted_at":"2012-10-17T05:32:20Z","abstract_excerpt":"An Ore extension over a polynomial algebra $\\mathbb{F}[x]$ is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra $\\mathsf{A}_h$ generated by elements $x,y$, which satisfy $yx-xy = h$, where $h\\in \\mathbb{F}[x]$. We investigate the family of algebras $\\mathsf{A}_h$ as $h$ ranges over all the polynomials in $\\mathbb{F}[x]$. When $h \\neq 0$, these algebras are subalgebras of the Weyl algebra $\\mathsf{A}_1$ and can be viewed as differential operators with polynomial coefficients. We give an exact description of the automorphisms of $\\mathsf{A}_h$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4631","kind":"arxiv","version":2},"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"}