{"paper":{"title":"Generalised Witt algebras and idealizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Susan J. Sierra, \\v{S}pela \\v{S}penko","submitted_at":"2016-10-03T22:35:47Z","abstract_excerpt":"Let $\\Bbbk$ be an algebraically closed field of characteristic zero, and let $\\Gamma$ be an additive subgroup of $\\Bbbk$. Results of Kaplansky-Santharoubane and Su classify intermediate series representations of the generalised Witt algebra $W_\\Gamma$ in terms of three families, one parameterised by ${\\mathbb A}^2$ and two by ${\\mathbb P}^1$. In this note, we use the first family to construct a homomorphism $\\Phi$ from the enveloping algebra $U(W_\\Gamma)$ to a skew extension of ${\\Bbbk}[a,b]$. We show that the image of $\\Phi$ is contained in a (double) idealizer subring of this skew extension "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00776","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"}