{"paper":{"title":"Braided enveloping algebras associated to quantum parabolic subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jan E. Grabowski","submitted_at":"2007-06-04T15:20:54Z","abstract_excerpt":"Associated to each subset $J$ of the nodes $I$ of a Dynkin diagram is a triangular decomposition of the corresponding Lie algebra $\\mathfrak{g}$ into three subalgebras $\\widetilde{\\mathfrak{g}_{J}}$ (generated by $e_{j}$, $f_{j}$ for $j\\in J$ and $h_{i}$ for $i\\in I$), $\\mathfrak{n}^{-}_{D}$ (generated by $f_{d}$, $d\\in D=I\\setminus J$) and its dual $\\mathfrak{n}_{D}^{+}$.\n  We demonstrate a quantum counterpart, generalising work of Majid and Rosso, by exhibiting analogous triangular decompositions of $U_{q}(\\mathfrak{g})$ and identifying a graded braided Hopf algebra that quantizes $\\mathfrak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0455","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"}