{"paper":{"title":"Classification of quantum groups and Lie bialgebra structures on $sl(n,\\mathbb{F})$. Relations with Brauer group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alexander Stolin, Iulia Pop","submitted_at":"2014-02-13T10:42:18Z","abstract_excerpt":"Given an arbitrary field $\\mathbb{F}$ of characteristic 0, we study Lie bialgebra structures on $sl(n,\\mathbb{F})$, based on the description of the corresponding classical double. For any Lie bialgebra structure $\\delta$, the classical double $D(sl(n,\\mathbb{F}),\\delta)$ is isomorphic to $sl(n,\\mathbb{F})\\otimes_{\\mathbb{F}} A$, where $A$ is either $\\mathbb{F}[\\varepsilon]$, with $\\varepsilon^{2}=0$, or $\\mathbb{F}\\oplus \\mathbb{F}$ or a quadratic field extension of $\\mathbb{F}$. In the first case, the classification leads to quasi-Frobenius Lie subalgebras of $sl(n,\\mathbb{F})$. In the second"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3083","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"}