{"paper":{"title":"Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Andrea Solotar, Samuel A. Lopes","submitted_at":"2019-03-04T13:29:13Z","abstract_excerpt":"For each nonzero $h\\in \\mathbb{F}[x]$, where $\\mathbb{F}$ is a field, let $\\mathsf{A}_h$ be the unital associative algebra generated by elements $x,y$, satisfying the relation $yx-xy = h$. This gives a parametric family of subalgebras of the Weyl algebra $\\mathsf{A}_1$, containing many well-known algebras which have previously been studied independently. In this paper, we give a full description the Hochschild cohomology $\\mathsf{HH}^\\bullet(\\mathsf{A}_h)$ over a field of arbitrary characteristic. In case $\\mathbb{F}$ has positive characteristic, the center of $\\mathsf{A}_h$ is nontrivial and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01226","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"}