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In sight of this, we prove two PBW-like theorems for $ F_q[SL(n+1)] $, both related to the classical PBW theorem for $ U({\\mathfrak{h}}) $."},"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":"q-alg/9701010","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-alg","submitted_at":"1997-01-10T16:12:54Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"06aced9245c59f68c3462fb5ad1fde40397cc25eded9cf72898de6093baf4d66","abstract_canon_sha256":"d4c87de3013554c2fdc70a36f421f66548dd5d9c529bbf00e592434a9a5ff6d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:42.853390Z","signature_b64":"9K6/l4SSaR1IhInzHE9wIWHHnnPfTGgYgto8TaKg+VrtiuZs5U4H/f47p97Ppfoym+q51HljVM3DknNTWiELCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d26c0fa2d65464747fd486b17bda618412298348ffc56758d53f466b7a209ff","last_reissued_at":"2026-05-18T00:44:42.852990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:42.852990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum function algebras as quantum enveloping algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Fabio Gavarini","submitted_at":"1997-01-10T16:12:54Z","abstract_excerpt":"Inspired by a result in [Ga], we locate two $ k[q,q^{-1}] $-integer forms of $ F_q[SL(n+1)] $, along with a presentation by generators and relations, and prove that for $ q=1 $ they specialize to $ U({\\mathfrak{h}}) $, where $ {\\mathfrak{h}} $ is the Lie bialgebra of the Poisson Lie group $ H $ dual of $ SL(n+1) $; moreover, we explain the relation with [loc. cit.]. 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