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We call any H in HA \"quantized function algebra\" (=QFA), resp. \"quantized (restricted) universal enveloping algebra\" (=QrUEA), at h if H/hH is the function algebra of a connected Poisson group, resp. the (restricted, if R/hR has positive characteristic) universal enveloping algebra of a (restricted) Lie bialgebra.\n  We establish an \"inner\" Galois' correspondence on HA, via the definition of two endofunctors, ()^\\vee and ()', of HA such that:\n  (a) the image"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0303019","kind":"arxiv","version":9},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-03-03T11:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"faac96aeadc205704cd870134bef014cb61786b37758605c9c5df539659cdbdf","abstract_canon_sha256":"2793044058def94199519e8a9fe56c65d09990a28e5d3def6405512669a8158c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:53.208327Z","signature_b64":"A7HfmzJaBqSif4+Mf/77fbQmScbbMKa3KvMzz2HRKdC15ELn2JCayJ7mAi315AqKfw88/knX5Y85qxHMxrcUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27fe5c5725227099319bc18d9af84dd482537ab6299740717dc92f11b684f0f8","last_reissued_at":"2026-05-18T03:43:53.207773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:53.207773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The global quantum duality principle: theory, examples, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fabio Gavarini (Universita` di Roma \"Tor Vergata\")","submitted_at":"2003-03-03T11:00:31Z","abstract_excerpt":"Let R be an integral domain, h non-zero in R such that R/hR is a field, and HA the category of torsionless (or flat) Hopf algebras over R. 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