{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:AQ232374R53QTIKU2QN6GXG2NT","short_pith_number":"pith:AQ232374","schema_version":"1.0","canonical_sha256":"0435bd6ffc8f7709a154d41be35cda6ceb8a385be85ab3b0915105717df8fa2c","source":{"kind":"arxiv","id":"2012.11927","version":4},"attestation_state":"computed","paper":{"title":"Periodic trivial extension algebras and fractionally Calabi-Yau algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Aaron Chan, Erik Darp\\\"o, Osamu Iyama, Ren\\'e Marczinzik","submitted_at":"2020-12-22T11:00:07Z","abstract_excerpt":"We study periodicity and twisted periodicity of the trivial extension algebra $T(A)$ of a finite-dimensional algebra $A$. Our main results show that (twisted) periodicity of $T(A)$ is equivalent to $A$ being (twisted) fractionally Calabi-Yau of finite global dimension. We also extend this result to a large class of self-injective orbit algebras. As a significant consequence, these results give a partial answer to the periodicity conjecture of Erdmann-Skowro\\'nski, which expects the classes of periodic and twisted periodic algebras to coincide. On the practical side, it allows us to construct a"},"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":"2012.11927","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-12-22T11:00:07Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"048aa301e253d019dd354c7c18e00cdec9aa7868c9de7d889f3da3fd6710b86e","abstract_canon_sha256":"dcfddce3c853398e85b0f545b009d9007824e3e0dd4a617a6f1d4b60e866a504"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:29.337534Z","signature_b64":"uK/gOumtS22g3yqysVVGdMab7lN3shjVaHpErfXaUTdx4tWcBaK9gKjCq0zEV1g9RRJEz5ie5IDoFYulCxxkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0435bd6ffc8f7709a154d41be35cda6ceb8a385be85ab3b0915105717df8fa2c","last_reissued_at":"2026-07-05T08:04:29.337056Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:29.337056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periodic trivial extension algebras and fractionally Calabi-Yau algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Aaron Chan, Erik Darp\\\"o, Osamu Iyama, Ren\\'e Marczinzik","submitted_at":"2020-12-22T11:00:07Z","abstract_excerpt":"We study periodicity and twisted periodicity of the trivial extension algebra $T(A)$ of a finite-dimensional algebra $A$. Our main results show that (twisted) periodicity of $T(A)$ is equivalent to $A$ being (twisted) fractionally Calabi-Yau of finite global dimension. We also extend this result to a large class of self-injective orbit algebras. As a significant consequence, these results give a partial answer to the periodicity conjecture of Erdmann-Skowro\\'nski, which expects the classes of periodic and twisted periodic algebras to coincide. On the practical side, it allows us to construct a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11927","kind":"arxiv","version":4},"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/2012.11927/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":"2012.11927","created_at":"2026-07-05T08:04:29.337113+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.11927v4","created_at":"2026-07-05T08:04:29.337113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11927","created_at":"2026-07-05T08:04:29.337113+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQ232374R53Q","created_at":"2026-07-05T08:04:29.337113+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQ232374R53QTIKU","created_at":"2026-07-05T08:04:29.337113+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQ232374","created_at":"2026-07-05T08:04:29.337113+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2103.15380","citing_title":"Classification of the d-representation-finite symmetric k-algebras of finite representation type","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2208.14413","citing_title":"The Derived Auslander-Iyama Correspondence","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08969","citing_title":"Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings","ref_index":113,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09082","citing_title":"Generation of immersed Lagrangians by cocores","ref_index":63,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT","json":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT.json","graph_json":"https://pith.science/api/pith-number/AQ232374R53QTIKU2QN6GXG2NT/graph.json","events_json":"https://pith.science/api/pith-number/AQ232374R53QTIKU2QN6GXG2NT/events.json","paper":"https://pith.science/paper/AQ232374"},"agent_actions":{"view_html":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT","download_json":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT.json","view_paper":"https://pith.science/paper/AQ232374","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.11927&json=true","fetch_graph":"https://pith.science/api/pith-number/AQ232374R53QTIKU2QN6GXG2NT/graph.json","fetch_events":"https://pith.science/api/pith-number/AQ232374R53QTIKU2QN6GXG2NT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT/action/storage_attestation","attest_author":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT/action/author_attestation","sign_citation":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT/action/citation_signature","submit_replication":"https://pith.science/pith/AQ232374R53QTIKU2QN6GXG2NT/action/replication_record"}},"created_at":"2026-07-05T08:04:29.337113+00:00","updated_at":"2026-07-05T08:04:29.337113+00:00"}