{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:JQKDRJXTIW275IFPQIGCDFWYKM","short_pith_number":"pith:JQKDRJXT","schema_version":"1.0","canonical_sha256":"4c1438a6f345b5fea0af820c2196d8531ff068b752f306a9729e4e2c7236126b","source":{"kind":"arxiv","id":"2108.08939","version":2},"attestation_state":"computed","paper":{"title":"Auslander's Theorem for dihedral actions on preprojective algebras of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jacob Barahona Kamsvaag, Jason Gaddis","submitted_at":"2021-08-19T23:02:04Z","abstract_excerpt":"Given an algebra $R$ and $G$ a finite group of automorphisms of $R$, there is a natural map $\\eta_{R,G}:R\\#G \\to \\mathrm{End}_{R^G} R$, called the Auslander map. A theorem of Auslander shows that $\\eta_{R,G}$ is an isomorphism when $R=\\mathbb{C}[V]$ and $G$ is a finite group acting linearly and without reflections on the finite-dimensional vector space $V$. The work of Mori and Bao-He-Zhang has encouraged study of this theorem in the context of Artin-Schelter regular algebras. We initiate a study of Auslander's result in the setting of non-connected graded Calabi-Yau algebras. When $R$ is a pr"},"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":"2108.08939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2021-08-19T23:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"1dadb1cd55c348907a5c56e524946f3f0abe0bec6cb248999165b1b6255fbb4f","abstract_canon_sha256":"fc5faef8634eb5a56c5f3a4b89ace366bbd1ab6b1409802311617abc0ad132e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:24:43.048100Z","signature_b64":"6aQ0Chm0q4tw+ybLLJSATNQ/XjXHOh7nA9qNBZ92L5ZvmLQBHT+Q8T9/9xWypuH7PjPdO0K3e/QCGMvTDMRRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c1438a6f345b5fea0af820c2196d8531ff068b752f306a9729e4e2c7236126b","last_reissued_at":"2026-07-05T06:24:43.047621Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:24:43.047621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Auslander's Theorem for dihedral actions on preprojective algebras of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jacob Barahona Kamsvaag, Jason Gaddis","submitted_at":"2021-08-19T23:02:04Z","abstract_excerpt":"Given an algebra $R$ and $G$ a finite group of automorphisms of $R$, there is a natural map $\\eta_{R,G}:R\\#G \\to \\mathrm{End}_{R^G} R$, called the Auslander map. A theorem of Auslander shows that $\\eta_{R,G}$ is an isomorphism when $R=\\mathbb{C}[V]$ and $G$ is a finite group acting linearly and without reflections on the finite-dimensional vector space $V$. The work of Mori and Bao-He-Zhang has encouraged study of this theorem in the context of Artin-Schelter regular algebras. We initiate a study of Auslander's result in the setting of non-connected graded Calabi-Yau algebras. When $R$ is a pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.08939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2108.08939","created_at":"2026-07-05T06:24:43.047687+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.08939v2","created_at":"2026-07-05T06:24:43.047687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.08939","created_at":"2026-07-05T06:24:43.047687+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQKDRJXTIW27","created_at":"2026-07-05T06:24:43.047687+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQKDRJXTIW275IFP","created_at":"2026-07-05T06:24:43.047687+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQKDRJXT","created_at":"2026-07-05T06:24:43.047687+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/JQKDRJXTIW275IFPQIGCDFWYKM","json":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM.json","graph_json":"https://pith.science/api/pith-number/JQKDRJXTIW275IFPQIGCDFWYKM/graph.json","events_json":"https://pith.science/api/pith-number/JQKDRJXTIW275IFPQIGCDFWYKM/events.json","paper":"https://pith.science/paper/JQKDRJXT"},"agent_actions":{"view_html":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM","download_json":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM.json","view_paper":"https://pith.science/paper/JQKDRJXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.08939&json=true","fetch_graph":"https://pith.science/api/pith-number/JQKDRJXTIW275IFPQIGCDFWYKM/graph.json","fetch_events":"https://pith.science/api/pith-number/JQKDRJXTIW275IFPQIGCDFWYKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM/action/storage_attestation","attest_author":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM/action/author_attestation","sign_citation":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM/action/citation_signature","submit_replication":"https://pith.science/pith/JQKDRJXTIW275IFPQIGCDFWYKM/action/replication_record"}},"created_at":"2026-07-05T06:24:43.047687+00:00","updated_at":"2026-07-05T06:24:43.047687+00:00"}