{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PAH6NMRVBDES5R235XOQZTU676","short_pith_number":"pith:PAH6NMRV","schema_version":"1.0","canonical_sha256":"780fe6b23508c92ec75beddd0cce9eff95f8e150c40a6b34da38c7decc0a3c4d","source":{"kind":"arxiv","id":"1211.6652","version":2},"attestation_state":"computed","paper":{"title":"*-Structures on Module-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Matthew Tucker-Simmons","submitted_at":"2012-11-28T16:49:55Z","abstract_excerpt":"This chapter lays out a framework for discussing (\\ast)-structures on module-algebras over a Hopf (\\ast)-algebra (H). We define a complex conjugation functor (V \\mapsto \\bar{V}), which is an involution on the module category (\\hmod), and discuss its interaction with natural constructions such as direct sums, duality, Hom, and tensor products. We define (\\ast)-structures first at the level of modules. We say that (V) is a (\\ast)-module if there is an isomorphism (\\ast : \\bar{V} \\to V) in (\\hmod) which is involutive in an appropriate sense. Then we define (\\ast)-structures on algebras in (\\hmod)"},"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":"1211.6652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-28T16:49:55Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"f05cb9e69da2b207d70df10e8ceb1c18311dda17050b5ac761d74da6046bb8f2","abstract_canon_sha256":"6eec94ef6fb7c3c215342332328bbd74012a1c30bd0097bcf22046bd4c43cc45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:06.061009Z","signature_b64":"rW9Qz6/6NDWuRq06n1JZ1x0ATwcbjaUr31vnEN6dyGXK9oTVfWU9KBGDVRZZ1Yd/bMZeb7AqKzdIWKwGB9YCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"780fe6b23508c92ec75beddd0cce9eff95f8e150c40a6b34da38c7decc0a3c4d","last_reissued_at":"2026-05-18T03:39:06.060227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:06.060227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"*-Structures on Module-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Matthew Tucker-Simmons","submitted_at":"2012-11-28T16:49:55Z","abstract_excerpt":"This chapter lays out a framework for discussing (\\ast)-structures on module-algebras over a Hopf (\\ast)-algebra (H). We define a complex conjugation functor (V \\mapsto \\bar{V}), which is an involution on the module category (\\hmod), and discuss its interaction with natural constructions such as direct sums, duality, Hom, and tensor products. We define (\\ast)-structures first at the level of modules. We say that (V) is a (\\ast)-module if there is an isomorphism (\\ast : \\bar{V} \\to V) in (\\hmod) which is involutive in an appropriate sense. Then we define (\\ast)-structures on algebras in (\\hmod)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6652","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":"1211.6652","created_at":"2026-05-18T03:39:06.060356+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.6652v2","created_at":"2026-05-18T03:39:06.060356+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6652","created_at":"2026-05-18T03:39:06.060356+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAH6NMRVBDES","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAH6NMRVBDES5R23","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAH6NMRV","created_at":"2026-05-18T12:27:18.751474+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/PAH6NMRVBDES5R235XOQZTU676","json":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676.json","graph_json":"https://pith.science/api/pith-number/PAH6NMRVBDES5R235XOQZTU676/graph.json","events_json":"https://pith.science/api/pith-number/PAH6NMRVBDES5R235XOQZTU676/events.json","paper":"https://pith.science/paper/PAH6NMRV"},"agent_actions":{"view_html":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676","download_json":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676.json","view_paper":"https://pith.science/paper/PAH6NMRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.6652&json=true","fetch_graph":"https://pith.science/api/pith-number/PAH6NMRVBDES5R235XOQZTU676/graph.json","fetch_events":"https://pith.science/api/pith-number/PAH6NMRVBDES5R235XOQZTU676/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676/action/storage_attestation","attest_author":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676/action/author_attestation","sign_citation":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676/action/citation_signature","submit_replication":"https://pith.science/pith/PAH6NMRVBDES5R235XOQZTU676/action/replication_record"}},"created_at":"2026-05-18T03:39:06.060356+00:00","updated_at":"2026-05-18T03:39:06.060356+00:00"}