{"paper":{"title":"Non-commutative Geometry of Homogenized Quantum $\\mathfrak{sl}(2,\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Alex Chirvasitu, Liang Ze Wong, S. Paul Smith","submitted_at":"2016-07-02T09:03:26Z","abstract_excerpt":"This paper examines the relationship between certain non-commutative analogues of projective 3-space, $\\mathbb{P}^3$, and the quantized enveloping algebras $U_q(\\mathfrak{sl}_2)$. The relationship is mediated by certain non-commutative graded algebras $S$, one for each $q \\in \\mathbb{C}^\\times$, having a degree-two central element $c$ such that $S[c^{-1}]_0 \\cong U_q(\\mathfrak{sl}_2)$. The non-commutative analogues of $\\mathbb{P}^3$ are the spaces $\\operatorname{Proj}_{nc}(S)$. We show how the points, fat points, lines, and quadrics, in $\\operatorname{Proj}_{nc}(S)$, and their incidence relati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00481","kind":"arxiv","version":2},"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"}