{"paper":{"title":"Construction of simple non-weight sl(2)-modules of arbitrary rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Carlos Tejero Prieto, Francisco J. Plaza Mart\\'in","submitted_at":"2016-02-02T16:22:41Z","abstract_excerpt":"We study simple non-weight ${\\mathfrak{sl}}(2)$-modules which are finitely generated as ${\\mathbb C}[z]$-modules. We show that they are described in terms of semilinear endomorphisms and prove that the Smith type induces a stratification on the set of these ${\\mathfrak{sl}}(2)$-modules, providing thus new invariants. Moreover, we show that there is a notion of duality for these type of ${\\mathfrak{sl}}(2)$-modules. Finally, we show that there are simple non-weight ${\\mathfrak{sl}}(2)$-modules of arbitrary rank by constructing a whole new family of them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00996","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"}