{"paper":{"title":"A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fiorela Rossi Bertone, Iv\\'an Angiono, Nicol\\'as Andruskiewitsch","submitted_at":"2016-03-30T21:15:16Z","abstract_excerpt":"Let $\\mathcal{B}_{\\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\\mathfrak{q} \\in \\mathbf{k}^{\\theta \\times \\theta}$, where $\\mathbf{k}$ is an algebraically closed field of characteristic 0. Let $\\mathcal{L}_{\\mathfrak{q}}$ be the Lusztig algebra associated to $\\mathcal{B}_{\\mathfrak{q}}$, see http://arxiv.org/abs/1501.04518. We present $\\mathcal{L}_{\\mathfrak{q}}$ as an extension (as braided Hopf algebras) of $\\mathcal{B}_{\\mathfrak{q}}$ by $\\mathfrak Z_{\\mathfrak{q}}$ where $\\mathfrak Z_{\\mathfrak{q}}$ is isomorphic to the universal envelop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09387","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"}