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We will obtain some basic properties of the two-parameter quantized enveloping algebra $U_{r,s}^{+}(\\mathfrak g)$. In particular, we will verify that the algebra $U_{r,s}^{+}(\\mathfrak g)$ satisfies many nice properties such as having normal separation, catenarity and Dixmier-Moeglin equivalence. We shall study a concrete example, the algebra $U_{r,s}^{+}(B_{2})$ in detail. We will first determine the normal ele"},"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":"1109.2640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-12T22:11:57Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"2752074cc7caa6c62b324a1370d4fb6c63e80173bcce8fc501a1d0dd8a0602a2","abstract_canon_sha256":"cbef7a724c3b04972b18061876a1f7fee28c1ab08e3d691491b94bed1b83401c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:08.002698Z","signature_b64":"sNImcfTZkR6W004WuC/gr6s/VfX//zD2Ow4XK2hDyGwHad/gyPrkXekxgiDgjpkl6gzv+Oe1mavpnzK5RyLgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1567dfa33281100b5e67860e21e0bf4fd1f569d753391842efd04a789c4f842","last_reissued_at":"2026-05-18T04:13:08.002023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:08.002023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Prime ideal Stratification and The Automorphism Group of $U^{+}_{r,s}(B_{2})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Xin Tang","submitted_at":"2011-09-12T22:11:57Z","abstract_excerpt":"Let ${\\mathfrak g}$ be a finite dimensional complex simple Lie algebra, and let $r,s\\in \\mathbb{C}^{\\ast}$ be transcendental over $\\mathbb{Q}$ such that $r^{m}s^{n}=1$ implies $m=n=0$. We will obtain some basic properties of the two-parameter quantized enveloping algebra $U_{r,s}^{+}(\\mathfrak g)$. In particular, we will verify that the algebra $U_{r,s}^{+}(\\mathfrak g)$ satisfies many nice properties such as having normal separation, catenarity and Dixmier-Moeglin equivalence. We shall study a concrete example, the algebra $U_{r,s}^{+}(B_{2})$ in detail. 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