{"paper":{"title":"A global quantum duality principle for subgroups and homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fabio Gavarini, Nicola Ciccoli","submitted_at":"2012-10-04T21:20:35Z","abstract_excerpt":"For a complex or real algebraic group G, with g:=Lie(G), quantizations of global type are suitable Hopf algebras F_q[G] or U_q(g) over C[q,q^{-1}]. Any such quantization yields a structure of Poisson group on G, and one of Lie bialgebra on g : correspondingly, one has dual Poisson groups G^* and a dual Lie bialgebra g^*. In this context, we introduce suitable notions of quantum subgroup and of quantum homogeneous space, in three versions: weak, proper and strict (also called \"flat\" in the literature). The last two notions only apply to those subgroups which are coisotropic, and those homogeneo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1597","kind":"arxiv","version":4},"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"}