{"paper":{"title":"Ideals in enveloping algebras of affine Kac-Moody algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Rekha Biswal, Susan J. Sierra","submitted_at":"2021-12-15T18:31:22Z","abstract_excerpt":"Let $L$ be an affine Kac-Moody algebra, with central element $c$, and let $\\lambda \\in \\mathbb C$. We study two-sided ideals in the central quotient $U_\\lambda(L):= U(L)/(c-\\lambda)$ of the universal enveloping algebra of $L$, and prove:\n  Theorem 1. If $\\lambda \\neq 0$ then $U_\\lambda(L)$ is simple.\n  Theorem 2. The algebra $U_0(L)$ has just-infinite growth, in the sense that any proper quotient has polynomial growth.\n  As an immediate corollary, we show that the annihilator of any nontrivial integrable highest weight representation of $L$ is centrally generated, extending a result of Chari f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.08334","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.08334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}