{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:IF6NCMPOSDB5LAOZ5BHON4VSV2","short_pith_number":"pith:IF6NCMPO","schema_version":"1.0","canonical_sha256":"417cd131ee90c3d581d9e84ee6f2b2aebe6c6ee6082a300f1360ce8696b0667c","source":{"kind":"arxiv","id":"math/0202101","version":1},"attestation_state":"computed","paper":{"title":"Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Mariano A. del Olmo, Oscar Arratia","submitted_at":"2002-02-12T09:07:32Z","abstract_excerpt":"Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (olmo01), to induce representations of quantum bicrossproduct algebras we construct the representations of the family of standard quantum inhomogeneous algebras $U_\\lambda(iso_{\\omega}(2))$. This family contains the quantum Euclidean, Galilei and Poincar\\'e algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on"},"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":"math/0202101","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-02-12T09:07:32Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2c0c06a9f8be60017e50c752e8dccb8176a9e3c22258879053deae384c04dc1e","abstract_canon_sha256":"64d0b3626eeb3141df55f7d2893156ed9fb4d9d55010e5945c418e3908112c31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:34.258636Z","signature_b64":"Fxa7JphP8bK87rkbbMAZAxBnSBHqI1LIihLcfbSuZnw8U7sk8hUxa1nMt7RnE/6sp0jDpnySRXi06VQz9mjPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"417cd131ee90c3d581d9e84ee6f2b2aebe6c6ee6082a300f1360ce8696b0667c","last_reissued_at":"2026-05-18T04:12:34.258088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:34.258088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Mariano A. del Olmo, Oscar Arratia","submitted_at":"2002-02-12T09:07:32Z","abstract_excerpt":"Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (olmo01), to induce representations of quantum bicrossproduct algebras we construct the representations of the family of standard quantum inhomogeneous algebras $U_\\lambda(iso_{\\omega}(2))$. This family contains the quantum Euclidean, Galilei and Poincar\\'e algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202101","kind":"arxiv","version":1},"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":"math/0202101","created_at":"2026-05-18T04:12:34.258158+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0202101v1","created_at":"2026-05-18T04:12:34.258158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202101","created_at":"2026-05-18T04:12:34.258158+00:00"},{"alias_kind":"pith_short_12","alias_value":"IF6NCMPOSDB5","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"IF6NCMPOSDB5LAOZ","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"IF6NCMPO","created_at":"2026-05-18T12:25:50.845339+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/IF6NCMPOSDB5LAOZ5BHON4VSV2","json":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2.json","graph_json":"https://pith.science/api/pith-number/IF6NCMPOSDB5LAOZ5BHON4VSV2/graph.json","events_json":"https://pith.science/api/pith-number/IF6NCMPOSDB5LAOZ5BHON4VSV2/events.json","paper":"https://pith.science/paper/IF6NCMPO"},"agent_actions":{"view_html":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2","download_json":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2.json","view_paper":"https://pith.science/paper/IF6NCMPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0202101&json=true","fetch_graph":"https://pith.science/api/pith-number/IF6NCMPOSDB5LAOZ5BHON4VSV2/graph.json","fetch_events":"https://pith.science/api/pith-number/IF6NCMPOSDB5LAOZ5BHON4VSV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2/action/storage_attestation","attest_author":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2/action/author_attestation","sign_citation":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2/action/citation_signature","submit_replication":"https://pith.science/pith/IF6NCMPOSDB5LAOZ5BHON4VSV2/action/replication_record"}},"created_at":"2026-05-18T04:12:34.258158+00:00","updated_at":"2026-05-18T04:12:34.258158+00:00"}