{"paper":{"title":"Geometrical Meaning of R-matrix Action for Quantum Groups at Roots of 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Fabio Gavarini","submitted_at":"1996-04-12T13:00:43Z","abstract_excerpt":"The present work splits in two parts: first, we perform a straightforward generalization of results from [Re], proving autoquasitriangularity of quantum groups $ U_q(\\frak{g}) $ and their unrestricted specializations at roots of 1, in particular the function algebra $ F[H] $ of the Poisson group $ H $ dual of $ G $; second, as a main contribution, we prove the convergence of the (specialized) $ R $--matrix action to a birational automorphism of a 2$\\ell$--fold ramified covering of the specialization of $ U_q(\\frak{g}) $ at a primitive $ \\ell $--th root of 1, and of a 2-fold ramified covering o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9604009","kind":"arxiv","version":5},"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"}