{"paper":{"title":"A quantum version of the algebra of distributions of $\\operatorname{SL}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Iv\\'an Angiono","submitted_at":"2016-07-17T13:33:19Z","abstract_excerpt":"Let $\\lambda$ be a primitive root of unity of order $\\ell$. We introduce a family of finite-dimensional algebras $\\{\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)\\}_{N\\in\\mathbb{N}_0}$ over the complex numbers, such that $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a subalgebra of $\\mathcal{D}_{\\lambda,M}(\\mathfrak{sl}_2)$ if $N<M$, and $\\mathcal{D}_{\\lambda,N-1}(\\mathfrak{sl}_2)\\subset \\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a $\\mathfrak{u}_{\\lambda}(\\mathfrak{sl}_2)$-cleft extension.\n  The simple $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$-modules $(\\mathcal{L}_{N}(p))_{0\\le p<\\ell^{N+1}}$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04869","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"}