{"paper":{"title":"Infinite Kostant cascades and centrally generated primitive ideals of $U(\\mathfrak{n})$ in types $A_{\\infty}$, $C_{\\infty}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ivan Penkov, Mikhail Ignatyev","submitted_at":"2015-02-19T07:41:46Z","abstract_excerpt":"We study the center of $U(\\mathfrak{n})$, where $\\mathfrak{n}$ is the locally nilpotent radical of a splitting Borel subalgebra of a simple complex Lie algebra $\\mathfrak{g}=\\mathfrak{sl}_{\\infty}(\\mathbb{C})$, $\\mathfrak{so}_{\\infty}(\\mathbb{C})$, $\\mathfrak{sp}_{\\infty}(\\mathbb{C})$. There are infinitely many isomorphism classes of Lie algebras $\\mathfrak{n}$, and we provide explicit generators of the center of $U(\\mathfrak{n})$ in all cases. We then fix $\\mathfrak{n}$ with \"largest possible\" center of $U(\\mathfrak{n})$ and characterize the centrally generated primitive ideals of $U(\\mathfra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05486","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"}