{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UNYVAUVFKRIYEFXYXMX2UM4CX7","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":"42cabd6b6f6f1a5f54c3e3d615acd8bda5e493526b2887acea021c3094019a07","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-23T22:32:12Z","title_canon_sha256":"c171e928b05e64c1a2eb66976fb22853c58ec5e67554e29f4b8f45b58dfddb42"},"schema_version":"1.0","source":{"id":"1211.5621","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5621","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5621v3","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5621","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"UNYVAUVFKRIY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNYVAUVFKRIYEFXY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNYVAUVF","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:f9dce21c56c34c3377123ac2ebfd850c38400d240c6e310b37c7cee80d0d7e77","target":"graph","created_at":"2026-05-18T02:51:23Z","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":"There is no systematic general procedure by which isomorphism classes of Hopf algebras that are extensions of $\\k F$ by ${\\k}^G$ can be found. We develop the general procedure for classification of isomorphism classes of Hopf algebras which are extensions of the group algebra $\\k C_p$ by ${\\k}^G$ where $C_p$ is a cyclic group of prime order $p$ and ${\\k}^G$ is the Hopf algebra dual of $\\k G$, $G$ a finite abelian $p$-group and $\\k$ is an algebraically closed field of characteristic $0$. We apply the method to calculate the number of isoclasses of commutative extensions and certain extensions o","authors_text":"Leonid Krop","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-23T22:32:12Z","title":"Isomorphism Types of Hopf Algebras in a Class of Abelian Extensions.I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5621","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:b3ee4c55dabd4297c54445b00e9df65f7451cb96573b02ba17bb721939b6da64","target":"record","created_at":"2026-05-18T02:51:23Z","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":"42cabd6b6f6f1a5f54c3e3d615acd8bda5e493526b2887acea021c3094019a07","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-23T22:32:12Z","title_canon_sha256":"c171e928b05e64c1a2eb66976fb22853c58ec5e67554e29f4b8f45b58dfddb42"},"schema_version":"1.0","source":{"id":"1211.5621","kind":"arxiv","version":3}},"canonical_sha256":"a3715052a554518216f8bb2faa3382bffa88f992060d287c5f2c8d401b960cea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3715052a554518216f8bb2faa3382bffa88f992060d287c5f2c8d401b960cea","first_computed_at":"2026-05-18T02:51:23.512529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:23.512529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ElCHJFI1yY3Vp6bDBONllKrcbWBhhJTS/+/xA54+udLStUQzh2VuME6R97PAaS7utJqGY/1M4IGlWO1Aj2nBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:23.513074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5621","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3ee4c55dabd4297c54445b00e9df65f7451cb96573b02ba17bb721939b6da64","sha256:f9dce21c56c34c3377123ac2ebfd850c38400d240c6e310b37c7cee80d0d7e77"],"state_sha256":"64d5e1aa4fd8739d1d968e3f9df668f77dbf633b711b4c8e0094a1dc68ff123f"}