{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZFSU5HGHPZFC6D62UMYJWLAK43","short_pith_number":"pith:ZFSU5HGH","schema_version":"1.0","canonical_sha256":"c9654e9cc77e4a2f0fdaa3309b2c0ae6d965c37d111ef0c3763ee4d217d9503f","source":{"kind":"arxiv","id":"1108.4648","version":1},"attestation_state":"computed","paper":{"title":"Oriented Involutions, Symmetric and Skew-Symmetric Elements in Group Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cesar Polcino Milies, Edgar G. Goodaire","submitted_at":"2011-08-23T16:23:22Z","abstract_excerpt":"Let $G$ be a group with involution * and $\\sigma\\colon G\\to\\{\\pm1\\}$ a group homomorphism. The map $\\sharp$ that sends $\\alpha=\\sum\\alpha_gg$ in a group ring $RG$ to $\\alpha^{\\sharp}=\\sum\\sigma(g)\\alpha_gg^*$ is an involution of $RG$ called an \\emph{oriented group involution}. An element $\\alpha\\in RG$ is \\emph{symmetric} if $\\alpha^{\\sharp}=\\alpha$ and \\emph{skew-symmetric} if $\\alpha^{\\sharp}=-\\alpha$. The sets of symmetric and skew-symmetric elements have received a lot of attention in the special cases that * is the inverse map on $G$ and/or $\\sigma$ is identically 1, but not in general. I"},"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":"1108.4648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-23T16:23:22Z","cross_cats_sorted":[],"title_canon_sha256":"7b12b72bb446fb069aa00044c8cb57b41811e5fafc23412ca19c5e46f2d4e86b","abstract_canon_sha256":"8e2fcd78882f3f948b3faee3103920b5f8144f5fd21b42016063e2820733dcf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:54.024400Z","signature_b64":"3mhrjMPZM5GzV3dTVqCdI8YzrN9afAKef6qxxYbYtlDCkYjVi0NephOKp692hMInhWClMOwQ0Vjo8xgfqFb3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9654e9cc77e4a2f0fdaa3309b2c0ae6d965c37d111ef0c3763ee4d217d9503f","last_reissued_at":"2026-05-18T04:14:54.023969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:54.023969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oriented Involutions, Symmetric and Skew-Symmetric Elements in Group Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cesar Polcino Milies, Edgar G. Goodaire","submitted_at":"2011-08-23T16:23:22Z","abstract_excerpt":"Let $G$ be a group with involution * and $\\sigma\\colon G\\to\\{\\pm1\\}$ a group homomorphism. The map $\\sharp$ that sends $\\alpha=\\sum\\alpha_gg$ in a group ring $RG$ to $\\alpha^{\\sharp}=\\sum\\sigma(g)\\alpha_gg^*$ is an involution of $RG$ called an \\emph{oriented group involution}. An element $\\alpha\\in RG$ is \\emph{symmetric} if $\\alpha^{\\sharp}=\\alpha$ and \\emph{skew-symmetric} if $\\alpha^{\\sharp}=-\\alpha$. The sets of symmetric and skew-symmetric elements have received a lot of attention in the special cases that * is the inverse map on $G$ and/or $\\sigma$ is identically 1, but not in general. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4648","kind":"arxiv","version":1},"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":"1108.4648","created_at":"2026-05-18T04:14:54.024034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.4648v1","created_at":"2026-05-18T04:14:54.024034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4648","created_at":"2026-05-18T04:14:54.024034+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZFSU5HGHPZFC","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZFSU5HGHPZFC6D62","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZFSU5HGH","created_at":"2026-05-18T12:26:47.523578+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/ZFSU5HGHPZFC6D62UMYJWLAK43","json":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43.json","graph_json":"https://pith.science/api/pith-number/ZFSU5HGHPZFC6D62UMYJWLAK43/graph.json","events_json":"https://pith.science/api/pith-number/ZFSU5HGHPZFC6D62UMYJWLAK43/events.json","paper":"https://pith.science/paper/ZFSU5HGH"},"agent_actions":{"view_html":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43","download_json":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43.json","view_paper":"https://pith.science/paper/ZFSU5HGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.4648&json=true","fetch_graph":"https://pith.science/api/pith-number/ZFSU5HGHPZFC6D62UMYJWLAK43/graph.json","fetch_events":"https://pith.science/api/pith-number/ZFSU5HGHPZFC6D62UMYJWLAK43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43/action/storage_attestation","attest_author":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43/action/author_attestation","sign_citation":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43/action/citation_signature","submit_replication":"https://pith.science/pith/ZFSU5HGHPZFC6D62UMYJWLAK43/action/replication_record"}},"created_at":"2026-05-18T04:14:54.024034+00:00","updated_at":"2026-05-18T04:14:54.024034+00:00"}