{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WMJRLO7UUW7HV7ER4OTM4DFQJO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5b310b0ef2f7d7690018a53df86fd44296a764d17475fe47b658ea0c2048833d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-19T22:25:11Z","title_canon_sha256":"0a2ed29b39d00f49a65a625f08341e83e3c3dfcf10ba82c567ec30b291ad9310"},"schema_version":"1.0","source":{"id":"1409.5824","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5824","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5824v3","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5824","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"pith_short_12","alias_value":"WMJRLO7UUW7H","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WMJRLO7UUW7HV7ER","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WMJRLO7U","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:3d5a8f5aa5021ed67e1edb484fe5544e5814b77f292fe4242db5e5c8a590d2ce","target":"graph","created_at":"2026-05-18T02:19:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article we construct a large family of $R$-matrices for various extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice and admit $R$-matrices in many cases where the original small quantum group does not. The results of this work extends some results that are well-known for $u_q(\\mathfrak{sl}_2)$. Especially for $A_n$ a combinatorial theorem about roots of unity was necessary, which is interesting on its own, and has been proven in a separate paper [LN14].","authors_text":"Daniel Nett, Simon Lentner","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-19T22:25:11Z","title":"New $R$-matrices for small quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5824","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a85fb06b6f0196aa4b94f22a0ea954a67612cb952a440b67336015124205afd7","target":"record","created_at":"2026-05-18T02:19:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5b310b0ef2f7d7690018a53df86fd44296a764d17475fe47b658ea0c2048833d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-19T22:25:11Z","title_canon_sha256":"0a2ed29b39d00f49a65a625f08341e83e3c3dfcf10ba82c567ec30b291ad9310"},"schema_version":"1.0","source":{"id":"1409.5824","kind":"arxiv","version":3}},"canonical_sha256":"b31315bbf4a5be7afc91e3a6ce0cb04b845dfe54d5795b01587bf4bb409baba0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b31315bbf4a5be7afc91e3a6ce0cb04b845dfe54d5795b01587bf4bb409baba0","first_computed_at":"2026-05-18T02:19:50.419414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:50.419414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"speLHApkmE/dViLZjvHuo1k7p3yFQIfJqzVzz2Oto1N+xrJN8eli60MDjNhLBOZKjvxk5Xh9abmSY6VPNcVdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:50.420078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5824","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a85fb06b6f0196aa4b94f22a0ea954a67612cb952a440b67336015124205afd7","sha256:3d5a8f5aa5021ed67e1edb484fe5544e5814b77f292fe4242db5e5c8a590d2ce"],"state_sha256":"3d23602ceac896928e7793c8fb2a8b3c9f76d25b4923040c2e430929db48e203"}