{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RJ34TB47K67QTCE3FB5ZWMTNWL","short_pith_number":"pith:RJ34TB47","canonical_record":{"source":{"id":"1501.05221","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-21T16:38:13Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"bfb351412abffd5481ac6033ddc8afd94a239652240579010d383f9398010355","abstract_canon_sha256":"d4f7daf2eaa0b2f7af11d9e9ac7ea00fd964d510f059bf7eca38a609526553d1"},"schema_version":"1.0"},"canonical_sha256":"8a77c9879f57bf09889b287b9b326db2fd8ac0f671897001040f2741fa6afb08","source":{"kind":"arxiv","id":"1501.05221","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05221","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05221v3","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05221","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"RJ34TB47K67Q","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RJ34TB47K67QTCE3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RJ34TB47","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RJ34TB47K67QTCE3FB5ZWMTNWL","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05221","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-21T16:38:13Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"bfb351412abffd5481ac6033ddc8afd94a239652240579010d383f9398010355","abstract_canon_sha256":"d4f7daf2eaa0b2f7af11d9e9ac7ea00fd964d510f059bf7eca38a609526553d1"},"schema_version":"1.0"},"canonical_sha256":"8a77c9879f57bf09889b287b9b326db2fd8ac0f671897001040f2741fa6afb08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:49.357561Z","signature_b64":"bPFYGALLmQkbqKaXu7NQ5MqW4JSJ6+/oC6/IHs8i1XZwsk1G+TUceohzGn8+jMlGXlG8kORytJ4sZdNKQmAyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a77c9879f57bf09889b287b9b326db2fd8ac0f671897001040f2741fa6afb08","last_reissued_at":"2026-05-18T01:09:49.356848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:49.356848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05221","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PTEGB+RBMIHd1+W3TGf5h/rXtoUSjYQqiR2YZZLQADkFgG/9WL50N4WAFl8HEeJWuhaCelxnfW7Z1IO6Zbl9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:55:23.801151Z"},"content_sha256":"aedbf84c25b2bbf81f7c6c25cfeb4d043989d4d62418fa29e0479ccb36e4777a","schema_version":"1.0","event_id":"sha256:aedbf84c25b2bbf81f7c6c25cfeb4d043989d4d62418fa29e0479ccb36e4777a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RJ34TB47K67QTCE3FB5ZWMTNWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Character groups of Hopf algebras as infinite-dimensional Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Alexander Schmeding, Geir Bogfjellmo, Rafael Dahmen","submitted_at":"2015-01-21T16:38:13Z","abstract_excerpt":"In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we construct an infinite-dimensional Lie group structure on the character group with values in a locally convex algebra. This structure turns the character group into a Baker--Campbell--Hausdorff--Lie group which is regular in the sense of Milnor. Furthermore, we show that certain subgroups associated to Hopf ideals become closed Lie subgroups of the character group.\n  If the Hopf algebra is not graded, its character group will in genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05221","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxc7KX2JrJiE0oVMnw/ik1gIOCRZhj0aDp9Wk97U7F1EmcWSM/UA+QKrfmd7SXlQe4zX66eZNcxwE6Hb3F+FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:55:23.801526Z"},"content_sha256":"2fe43da4a779688d633ebe85e38c2ebb3bec8901bc75357a1bc4c13ae172e41a","schema_version":"1.0","event_id":"sha256:2fe43da4a779688d633ebe85e38c2ebb3bec8901bc75357a1bc4c13ae172e41a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJ34TB47K67QTCE3FB5ZWMTNWL/bundle.json","state_url":"https://pith.science/pith/RJ34TB47K67QTCE3FB5ZWMTNWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJ34TB47K67QTCE3FB5ZWMTNWL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T09:55:23Z","links":{"resolver":"https://pith.science/pith/RJ34TB47K67QTCE3FB5ZWMTNWL","bundle":"https://pith.science/pith/RJ34TB47K67QTCE3FB5ZWMTNWL/bundle.json","state":"https://pith.science/pith/RJ34TB47K67QTCE3FB5ZWMTNWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJ34TB47K67QTCE3FB5ZWMTNWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RJ34TB47K67QTCE3FB5ZWMTNWL","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":"d4f7daf2eaa0b2f7af11d9e9ac7ea00fd964d510f059bf7eca38a609526553d1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-21T16:38:13Z","title_canon_sha256":"bfb351412abffd5481ac6033ddc8afd94a239652240579010d383f9398010355"},"schema_version":"1.0","source":{"id":"1501.05221","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05221","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05221v3","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05221","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"RJ34TB47K67Q","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RJ34TB47K67QTCE3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RJ34TB47","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:2fe43da4a779688d633ebe85e38c2ebb3bec8901bc75357a1bc4c13ae172e41a","target":"graph","created_at":"2026-05-18T01:09:49Z","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":"In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we construct an infinite-dimensional Lie group structure on the character group with values in a locally convex algebra. This structure turns the character group into a Baker--Campbell--Hausdorff--Lie group which is regular in the sense of Milnor. Furthermore, we show that certain subgroups associated to Hopf ideals become closed Lie subgroups of the character group.\n  If the Hopf algebra is not graded, its character group will in genera","authors_text":"Alexander Schmeding, Geir Bogfjellmo, Rafael Dahmen","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-21T16:38:13Z","title":"Character groups of Hopf algebras as infinite-dimensional Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05221","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:aedbf84c25b2bbf81f7c6c25cfeb4d043989d4d62418fa29e0479ccb36e4777a","target":"record","created_at":"2026-05-18T01:09:49Z","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":"d4f7daf2eaa0b2f7af11d9e9ac7ea00fd964d510f059bf7eca38a609526553d1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-21T16:38:13Z","title_canon_sha256":"bfb351412abffd5481ac6033ddc8afd94a239652240579010d383f9398010355"},"schema_version":"1.0","source":{"id":"1501.05221","kind":"arxiv","version":3}},"canonical_sha256":"8a77c9879f57bf09889b287b9b326db2fd8ac0f671897001040f2741fa6afb08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a77c9879f57bf09889b287b9b326db2fd8ac0f671897001040f2741fa6afb08","first_computed_at":"2026-05-18T01:09:49.356848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:49.356848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPFYGALLmQkbqKaXu7NQ5MqW4JSJ6+/oC6/IHs8i1XZwsk1G+TUceohzGn8+jMlGXlG8kORytJ4sZdNKQmAyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:49.357561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05221","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aedbf84c25b2bbf81f7c6c25cfeb4d043989d4d62418fa29e0479ccb36e4777a","sha256:2fe43da4a779688d633ebe85e38c2ebb3bec8901bc75357a1bc4c13ae172e41a"],"state_sha256":"4361e77d71fef47b87f12f28872ac9fb76722663e9f1ec4d1d8f71b9a4f0ab85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bL7srAuFpHrvxjqjLfiMW16TWxJaIfnAOGR2XYEWkTJkPRHrFZurXpCyMcMOnasBbsTw+UghJbTn3mx0EIZeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:55:23.803690Z","bundle_sha256":"b2c6034915df5d2950d11ad3e1bccf7dcc597ac6cba8db838ce5fce626e927e8"}}