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If $q$ has a finite multiplicative order $t>4,$ this classification remains valid for homogeneous right coideal subalgebras of the small Lusztig quantum group $u_q^+(\\frak{so}_{2n+1}).$ As a consequence, we determine that the total number of right coideal subalgebras that contain the coradical equals $(2n)!!,$ the order of the Weyl group defined by the root system of type $B_n.$"},"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":"0908.4235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-08-28T16:22:57Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"1f51efcde8152f43e6065dfb1f324120fedb36ff0a9ee783272de2c3b130a9e5","abstract_canon_sha256":"3e7f4a15ccf1b0ba4c481830832984eac0384fe889437c92fe24bd0fbc9597d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:48:35.895242Z","signature_b64":"7PRR1rPcufXM3rWkeu6aL7rDVqwLEQnhgRICY+n9iphv8cFNu9gcdkBdlpB5C4O02a1sd2BZE012t5DKqYGoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2cd422ec0b69458497a12f76c68bccca401751cf5132fc68835aeb74bb1cd76","last_reissued_at":"2026-07-04T15:48:35.894903Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:48:35.894903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Right coideal subalgebras in U^+_q(so_{2n+1})","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Vladislav Kharchenko","submitted_at":"2009-08-28T16:22:57Z","abstract_excerpt":"We give a complete classification of right coideal subalgebras that contain all group-like elements for the quantum group $U_q^+(\\frak{so}_{2n+1}),$ provided that $q$ is not a root of 1. 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