{"paper":{"title":"Primitive ideals of $\\operatorname{U}(\\frak{sl}(\\infty))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Alexey Petukhov, Ivan Penkov","submitted_at":"2016-08-31T16:39:52Z","abstract_excerpt":"We provide an explicit description of the primitive ideals of the enveloping algebra $\\operatorname{U}(\\frak{sl}(\\infty))$ of the infinite-dimensional finitary Lie algebra $\\frak{sl}(\\infty)$ over an uncountable algebraically closed field of characteristic 0. Our main new result is that any primitive ideal of $\\operatorname{U}(\\frak{sl}(\\infty))$ is integrable. A classification of integrable primitive ideals of $\\operatorname{U}(\\frak{sl}(\\infty))$ has been known previously, and relies on the pioneering work of A. Zhilinskii."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08934","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":""},"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"}