{"paper":{"title":"A class of non-weight modules over the Schr\\\"{o}dinger-Virasoro algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Honglian Zhang, Yumei Wang","submitted_at":"2018-09-14T02:56:56Z","abstract_excerpt":"We construct and classify the free $U(\\mathbb{C}L_0\\oplus \\mathbb{C}M_0\\oplus\\mathbb{C}Y_0)$-modules of rank $1$ over the Schr\\\"{o}dinger-Virasoro algebra $\\mathfrak{sv}(s)$ for $s=0$.Moreover, we show that the class of free $U(\\mathbb{C}L_0\\oplus\\mathbb{C}M_0)$-modules of rank $1$ over the Schr\\\"{o}dinger-Virasoro algebra $\\mathfrak{sv}(s)$ for $s=\\frac{1}{2}$ is nonexistent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05236","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"}