{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YES3PNQ6VWAJWDKF3LQIXHKP53","short_pith_number":"pith:YES3PNQ6","schema_version":"1.0","canonical_sha256":"c125b7b61ead809b0d45dae08b9d4feee2d093d1bff28369be66c0d72799f9a8","source":{"kind":"arxiv","id":"1702.02841","version":2},"attestation_state":"computed","paper":{"title":"Universal deformation rings and self-injective Nakayama algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Daniel J. Wackwitz, Frauke M. Bleher","submitted_at":"2017-02-09T14:17:51Z","abstract_excerpt":"Let $k$ be a field and let $\\Lambda$ be an indecomposable finite dimensional $k$-algebra such that there is a stable equivalence of Morita type between $\\Lambda$ and a self-injective split basic Nakayama algebra over $k$. We show that every indecomposable finitely generated $\\Lambda$-module $V$ has a universal deformation ring $R(\\Lambda,V)$ and we describe $R(\\Lambda,V)$ explicitly as a quotient ring of a power series ring over $k$ in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to $p$-modular blocks of finite groups with cyclic defect groups."},"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":"1702.02841","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-09T14:17:51Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9e4aaa39b04d2706607df5b63f8cc658639d4943f254c29bbf127ed34a26b8e5","abstract_canon_sha256":"068dfd857ff05137280b2e3ba118f0ddd60f29905138457d00bcfeef08ebc3b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:00.399151Z","signature_b64":"BbHIbUVnE6z8TvzVr9VQbT1hK1Hr2yLbiir+MVcCVYL2WLhWGo8mcruWh4CckoiObAD5Acf29sKAqCzkUc75Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c125b7b61ead809b0d45dae08b9d4feee2d093d1bff28369be66c0d72799f9a8","last_reissued_at":"2026-05-17T23:51:00.398644Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:00.398644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal deformation rings and self-injective Nakayama algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Daniel J. Wackwitz, Frauke M. Bleher","submitted_at":"2017-02-09T14:17:51Z","abstract_excerpt":"Let $k$ be a field and let $\\Lambda$ be an indecomposable finite dimensional $k$-algebra such that there is a stable equivalence of Morita type between $\\Lambda$ and a self-injective split basic Nakayama algebra over $k$. We show that every indecomposable finitely generated $\\Lambda$-module $V$ has a universal deformation ring $R(\\Lambda,V)$ and we describe $R(\\Lambda,V)$ explicitly as a quotient ring of a power series ring over $k$ in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to $p$-modular blocks of finite groups with cyclic defect groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02841","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":"1702.02841","created_at":"2026-05-17T23:51:00.398716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.02841v2","created_at":"2026-05-17T23:51:00.398716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02841","created_at":"2026-05-17T23:51:00.398716+00:00"},{"alias_kind":"pith_short_12","alias_value":"YES3PNQ6VWAJ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YES3PNQ6VWAJWDKF","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YES3PNQ6","created_at":"2026-05-18T12:31:56.362134+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/YES3PNQ6VWAJWDKF3LQIXHKP53","json":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53.json","graph_json":"https://pith.science/api/pith-number/YES3PNQ6VWAJWDKF3LQIXHKP53/graph.json","events_json":"https://pith.science/api/pith-number/YES3PNQ6VWAJWDKF3LQIXHKP53/events.json","paper":"https://pith.science/paper/YES3PNQ6"},"agent_actions":{"view_html":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53","download_json":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53.json","view_paper":"https://pith.science/paper/YES3PNQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.02841&json=true","fetch_graph":"https://pith.science/api/pith-number/YES3PNQ6VWAJWDKF3LQIXHKP53/graph.json","fetch_events":"https://pith.science/api/pith-number/YES3PNQ6VWAJWDKF3LQIXHKP53/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53/action/storage_attestation","attest_author":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53/action/author_attestation","sign_citation":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53/action/citation_signature","submit_replication":"https://pith.science/pith/YES3PNQ6VWAJWDKF3LQIXHKP53/action/replication_record"}},"created_at":"2026-05-17T23:51:00.398716+00:00","updated_at":"2026-05-17T23:51:00.398716+00:00"}