{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FWP3HEW7UXJIDX6VLO2ITXCOYT","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":"82a3d9460ccead3b2026a6f1541b17b2f1e0ab2ab22f7058bb40f6acdf9d38fd","cross_cats_sorted":["math.KT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-03T13:36:40Z","title_canon_sha256":"a88d55f7016026cb567dfaa4f4849be26f74627c2ce1e8a18641a49fb76cef15"},"schema_version":"1.0","source":{"id":"1204.0687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0687","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0687v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0687","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"FWP3HEW7UXJI","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FWP3HEW7UXJIDX6V","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FWP3HEW7","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:46b181ffd7c9f51cf096532b276ba60e27b8d6c1bca99043ac4bcc85e1e1f53f","target":"graph","created_at":"2026-05-17T23:53:18Z","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":"We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor categories of comodules, then one can transport what we call a free Yetter-Drinfeld resolution of the counit of $A$ to the same kind of resolution for the counit of $H$, exhibiting in this way strong links between the Hochschild homologies of $A$ and $H$. This enables us to get a finite free resolution of the counit of $\\mathcal B(E)$, the Hopf algebra of the bilinear form associated to an invertible matrix $E$, generalizing an ealier construction of Collins, Hartel and Thom in the orthogonal case $E=I_n$. It follows tha","authors_text":"Julien Bichon","cross_cats":["math.KT","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-03T13:36:40Z","title":"Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0687","kind":"arxiv","version":1},"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:acade1a6d720ea4765de98764898508170fe63ab89957c7170d059a21642c21f","target":"record","created_at":"2026-05-17T23:53:18Z","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":"82a3d9460ccead3b2026a6f1541b17b2f1e0ab2ab22f7058bb40f6acdf9d38fd","cross_cats_sorted":["math.KT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-03T13:36:40Z","title_canon_sha256":"a88d55f7016026cb567dfaa4f4849be26f74627c2ce1e8a18641a49fb76cef15"},"schema_version":"1.0","source":{"id":"1204.0687","kind":"arxiv","version":1}},"canonical_sha256":"2d9fb392dfa5d281dfd55bb489dc4ec4eec26d8671f54f9dcef1c0252bf76e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d9fb392dfa5d281dfd55bb489dc4ec4eec26d8671f54f9dcef1c0252bf76e19","first_computed_at":"2026-05-17T23:53:18.809616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.809616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WCywnFRMGJn7QNByQm2N8laqI31KB+KLAak+MERWiLFklYHQAampHtKZixEArtQz46gbRMaEhqP5Uin+Lw8PBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.810237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acade1a6d720ea4765de98764898508170fe63ab89957c7170d059a21642c21f","sha256:46b181ffd7c9f51cf096532b276ba60e27b8d6c1bca99043ac4bcc85e1e1f53f"],"state_sha256":"e29f0955cdd49857347854eebd992510af5839d4ccc0cb87a65366646c454968"}