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Tolstoy","submitted_at":"2016-12-12T19:42:46Z","abstract_excerpt":"Using the isomorphism $\\mathfrak{o}(3;\\mathbb{C})\\simeq\\mathfrak{sl}(2;\\mathbb{C})$ we develop a new simple algebraic technique for complete classification of quantum deformations (the classical $r$-matrices) for real forms $\\mathfrak{o}(3)$ and $\\mathfrak{o}(2,1)$ of the complex Lie algebra $\\mathfrak{o}(3;\\mathbb{C})$ in terms of real forms of $\\mathfrak{sl}(2;\\mathbb{C})$: $\\mathfrak{su}(2)$, $\\mathfrak{su}(1,1)$ and $\\mathfrak{sl}(2;\\mathbb{R})$. We prove that the $D=3$ Lorentz symmetry $\\mathfrak{o}(2,1)\\simeq\\mathfrak{su}(1,1)\\simeq\\mathfrak{sl}(2;\\mathbb{R})$ has three different Hopf-al"},"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":"1612.03866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-12T19:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"2e1ac8a3316d971bfa1205c6b907a10ad035d5fd2573cb1e71e16718ea9e845a","abstract_canon_sha256":"c8bf4f53b5a6cebd5e2bf0de950be755d36b78a5d0b06ac6a97dca478138e8be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:44.214832Z","signature_b64":"Yn+GQBaVVcIvMoeXGoDC2M4eFrNmDNo+1xw5g5jts5rjkpmmwBvrcReVD0sE+ETaOWLTyU1AqADuN2OjtWdZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc843f2e135d8df84432d94ec857422f310bc918efe79c122bf3eb32a9ec9d18","last_reissued_at":"2026-05-18T00:45:44.214157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:44.214157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantizations of D=3 Lorentz symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"J. Lukierski, V.N. Tolstoy","submitted_at":"2016-12-12T19:42:46Z","abstract_excerpt":"Using the isomorphism $\\mathfrak{o}(3;\\mathbb{C})\\simeq\\mathfrak{sl}(2;\\mathbb{C})$ we develop a new simple algebraic technique for complete classification of quantum deformations (the classical $r$-matrices) for real forms $\\mathfrak{o}(3)$ and $\\mathfrak{o}(2,1)$ of the complex Lie algebra $\\mathfrak{o}(3;\\mathbb{C})$ in terms of real forms of $\\mathfrak{sl}(2;\\mathbb{C})$: $\\mathfrak{su}(2)$, $\\mathfrak{su}(1,1)$ and $\\mathfrak{sl}(2;\\mathbb{R})$. We prove that the $D=3$ Lorentz symmetry $\\mathfrak{o}(2,1)\\simeq\\mathfrak{su}(1,1)\\simeq\\mathfrak{sl}(2;\\mathbb{R})$ has three different Hopf-al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03866","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.03866","created_at":"2026-05-18T00:45:44.214252+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.03866v2","created_at":"2026-05-18T00:45:44.214252+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03866","created_at":"2026-05-18T00:45:44.214252+00:00"},{"alias_kind":"pith_short_12","alias_value":"7SCD6LQTLWG7","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7SCD6LQTLWG7QRBS","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7SCD6LQT","created_at":"2026-05-18T12:30:04.600751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4","json":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4.json","graph_json":"https://pith.science/api/pith-number/7SCD6LQTLWG7QRBS3FHMQV2CF4/graph.json","events_json":"https://pith.science/api/pith-number/7SCD6LQTLWG7QRBS3FHMQV2CF4/events.json","paper":"https://pith.science/paper/7SCD6LQT"},"agent_actions":{"view_html":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4","download_json":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4.json","view_paper":"https://pith.science/paper/7SCD6LQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.03866&json=true","fetch_graph":"https://pith.science/api/pith-number/7SCD6LQTLWG7QRBS3FHMQV2CF4/graph.json","fetch_events":"https://pith.science/api/pith-number/7SCD6LQTLWG7QRBS3FHMQV2CF4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4/action/storage_attestation","attest_author":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4/action/author_attestation","sign_citation":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4/action/citation_signature","submit_replication":"https://pith.science/pith/7SCD6LQTLWG7QRBS3FHMQV2CF4/action/replication_record"}},"created_at":"2026-05-18T00:45:44.214252+00:00","updated_at":"2026-05-18T00:45:44.214252+00:00"}