{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AIY2OPRRFELWMOWDHBZ66PWLFO","short_pith_number":"pith:AIY2OPRR","schema_version":"1.0","canonical_sha256":"0231a73e312917663ac33873ef3ecb2b82dedce9699bd9b5ee81fba7dd61bfc3","source":{"kind":"arxiv","id":"1812.05071","version":2},"attestation_state":"computed","paper":{"title":"From a Kac algebra subfactor to Drinfeld double","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sandipan De","submitted_at":"2018-12-12T18:17:50Z","abstract_excerpt":"Given a finite-index and finite-depth subfactor, we define the notion of \\textit{quantum double inclusion} - a certain unital inclusion of von Neumann algebras constructed from the given subfactor - which is closely related to that of Ocneanu's asymptotic inclusion. We show that the quantum double inclusion when applied to the Kac algebra subfactor $R^H \\subset R$ produces Drinfeld double of $H$ where $H$ is a finite-dimensional Kac algebra acting outerly on the hyperfinite $II_1$ factor $R$ and $R^H$ denotes the fixed-point subalgebra. More precisely, quantum double inclusion of $R^H \\subset "},"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":"1812.05071","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OA","submitted_at":"2018-12-12T18:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"442b2a5d452271e4b2044f23a2a10ec67892b5538e6048f73f00d926b918d985","abstract_canon_sha256":"ae2521e69afb1a1efc9f5cdec9e5fb174350eb663a6295d4964a44e3414a9000"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:57.646636Z","signature_b64":"qf5ePokBQE6973nTlYOIYMwpbMW2KL2HVIhC6XItI9MPXBNSxwiFzTlQn2DrlZjNV0e9QxMHEG07NZv5WzUGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0231a73e312917663ac33873ef3ecb2b82dedce9699bd9b5ee81fba7dd61bfc3","last_reissued_at":"2026-05-17T23:39:57.646164Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:57.646164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From a Kac algebra subfactor to Drinfeld double","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sandipan De","submitted_at":"2018-12-12T18:17:50Z","abstract_excerpt":"Given a finite-index and finite-depth subfactor, we define the notion of \\textit{quantum double inclusion} - a certain unital inclusion of von Neumann algebras constructed from the given subfactor - which is closely related to that of Ocneanu's asymptotic inclusion. We show that the quantum double inclusion when applied to the Kac algebra subfactor $R^H \\subset R$ produces Drinfeld double of $H$ where $H$ is a finite-dimensional Kac algebra acting outerly on the hyperfinite $II_1$ factor $R$ and $R^H$ denotes the fixed-point subalgebra. More precisely, quantum double inclusion of $R^H \\subset "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05071","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":"1812.05071","created_at":"2026-05-17T23:39:57.646241+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.05071v2","created_at":"2026-05-17T23:39:57.646241+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05071","created_at":"2026-05-17T23:39:57.646241+00:00"},{"alias_kind":"pith_short_12","alias_value":"AIY2OPRRFELW","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AIY2OPRRFELWMOWD","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AIY2OPRR","created_at":"2026-05-18T12:32:13.499390+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/AIY2OPRRFELWMOWDHBZ66PWLFO","json":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO.json","graph_json":"https://pith.science/api/pith-number/AIY2OPRRFELWMOWDHBZ66PWLFO/graph.json","events_json":"https://pith.science/api/pith-number/AIY2OPRRFELWMOWDHBZ66PWLFO/events.json","paper":"https://pith.science/paper/AIY2OPRR"},"agent_actions":{"view_html":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO","download_json":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO.json","view_paper":"https://pith.science/paper/AIY2OPRR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.05071&json=true","fetch_graph":"https://pith.science/api/pith-number/AIY2OPRRFELWMOWDHBZ66PWLFO/graph.json","fetch_events":"https://pith.science/api/pith-number/AIY2OPRRFELWMOWDHBZ66PWLFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO/action/storage_attestation","attest_author":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO/action/author_attestation","sign_citation":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO/action/citation_signature","submit_replication":"https://pith.science/pith/AIY2OPRRFELWMOWDHBZ66PWLFO/action/replication_record"}},"created_at":"2026-05-17T23:39:57.646241+00:00","updated_at":"2026-05-17T23:39:57.646241+00:00"}