{"paper":{"title":"Quantum algebras as quantizations of dual Poisson-Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Angel Ballesteros, Fabio Musso","submitted_at":"2012-12-16T17:38:36Z","abstract_excerpt":"A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\\Delta_z) starting from the Lie bialgebra (g,\\delta) that gives the first-order deformation of the coproduct map \\Delta_z is presented. The procedure is based on the fact that any quantum algebra can be viewed as the quantization of the unique Poisson-Lie structure (G^\\ast,\\Lambda_g) on the dual group G^\\ast, which is obtained by exponentiating the Lie algebra g^\\ast defined by the dual map \\delta^\\ast. From this perspective, the coproduct for U_z(g) is just the pullback of the group law for G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3809","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"}