{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EPGJPM46TJOFB4ZRWVKELKBCQY","short_pith_number":"pith:EPGJPM46","schema_version":"1.0","canonical_sha256":"23cc97b39e9a5c50f331b55445a822862e0afa4f999bd3fd7908c4a8071f50d3","source":{"kind":"arxiv","id":"1303.7203","version":2},"attestation_state":"computed","paper":{"title":"Quantum binary polyhedral groups and their actions on quantum planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Chelsea Walton, Ellen Kirkman, James Zhang, Kenneth Chan","submitted_at":"2013-03-28T18:50:24Z","abstract_excerpt":"We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner faithfully and preserves the grading of an Artin-Schelter regular algebra R of global dimension two. Remarkably, the corresponding invariant rings R^H share similar regularity and Gorenstein properties as the invariant rings k[u,v]^G in the classic setting. We also present several questions and directions for expanding this work in noncommutative invariant theory"},"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":"1303.7203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-03-28T18:50:24Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"4fb279f52646295967d8388a058add93b0c5c4aa6f76f8a3cd6b9f94bae2a167","abstract_canon_sha256":"d53a6cf98c22cfba5e56e3d93ce3529b722c8e27d34634518e6e5260aa06786b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:27.428520Z","signature_b64":"dMoRk5nChXL2q/OSJhlxK3njrBNopHEf2ZcTFCbXq1vQNtvjurJCk8z+P1Vs5hyxLWk/4PSe0YsDpXQW7l6+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23cc97b39e9a5c50f331b55445a822862e0afa4f999bd3fd7908c4a8071f50d3","last_reissued_at":"2026-05-18T02:48:27.427985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:27.427985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum binary polyhedral groups and their actions on quantum planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Chelsea Walton, Ellen Kirkman, James Zhang, Kenneth Chan","submitted_at":"2013-03-28T18:50:24Z","abstract_excerpt":"We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner faithfully and preserves the grading of an Artin-Schelter regular algebra R of global dimension two. Remarkably, the corresponding invariant rings R^H share similar regularity and Gorenstein properties as the invariant rings k[u,v]^G in the classic setting. We also present several questions and directions for expanding this work in noncommutative invariant theory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7203","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":"1303.7203","created_at":"2026-05-18T02:48:27.428057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.7203v2","created_at":"2026-05-18T02:48:27.428057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7203","created_at":"2026-05-18T02:48:27.428057+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPGJPM46TJOF","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPGJPM46TJOFB4ZR","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPGJPM46","created_at":"2026-05-18T12:27:43.054852+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/EPGJPM46TJOFB4ZRWVKELKBCQY","json":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY.json","graph_json":"https://pith.science/api/pith-number/EPGJPM46TJOFB4ZRWVKELKBCQY/graph.json","events_json":"https://pith.science/api/pith-number/EPGJPM46TJOFB4ZRWVKELKBCQY/events.json","paper":"https://pith.science/paper/EPGJPM46"},"agent_actions":{"view_html":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY","download_json":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY.json","view_paper":"https://pith.science/paper/EPGJPM46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.7203&json=true","fetch_graph":"https://pith.science/api/pith-number/EPGJPM46TJOFB4ZRWVKELKBCQY/graph.json","fetch_events":"https://pith.science/api/pith-number/EPGJPM46TJOFB4ZRWVKELKBCQY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY/action/storage_attestation","attest_author":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY/action/author_attestation","sign_citation":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY/action/citation_signature","submit_replication":"https://pith.science/pith/EPGJPM46TJOFB4ZRWVKELKBCQY/action/replication_record"}},"created_at":"2026-05-18T02:48:27.428057+00:00","updated_at":"2026-05-18T02:48:27.428057+00:00"}