{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V4VXWSQQHXWCI7NJCGP6OTTHXN","short_pith_number":"pith:V4VXWSQQ","schema_version":"1.0","canonical_sha256":"af2b7b4a103dec247da9119fe74e67bb61be74a2b5c23eaeaa67b4c7f9d383fb","source":{"kind":"arxiv","id":"1804.01168","version":1},"attestation_state":"computed","paper":{"title":"Cokernels of the Cartan Matrix and Stratifying Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Corina S\\'aenz, Eduardo Marcos, Octavio Mendoza","submitted_at":"2018-04-03T20:58:47Z","abstract_excerpt":"We study the cokernel of the application given by the Cartan Matrix $C_\\Lambda$ of a finite dimensional $k$-algebra $\\Lambda.$ This produces a finitely generated abelian group, the Cartan group $G_\\Lambda,$ which is invariant under derived equivalences. We are interested in the case when $G_\\Lambda$ is finite. For a standardly stratified algebra, it is shown that this group is always finite and some interesting connections with the standard modules are found. As a consequence, it is got that $G_\\Lambda$ can be seen as a measure of how far is a standardly stratified algebra $\\Lambda$ to be quas"},"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":"1804.01168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-04-03T20:58:47Z","cross_cats_sorted":[],"title_canon_sha256":"6cf3e865df508ee04b37c4f204a61277c8682a26ad320ee0746ecc3f1ba1e1a5","abstract_canon_sha256":"967c590b2977b849ef2efe22ab5df94d30b608b1feff26fd225589db9d516366"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:15.880758Z","signature_b64":"y2xn7MuUIQOf3rj7wQdPVOFePbIS7XwncjDXBXkAVnJxZJL5TZW/SQx2PfE626oTWDxbWvBmdCTUH2AC9+9UAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af2b7b4a103dec247da9119fe74e67bb61be74a2b5c23eaeaa67b4c7f9d383fb","last_reissued_at":"2026-05-18T00:19:15.880175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:15.880175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cokernels of the Cartan Matrix and Stratifying Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Corina S\\'aenz, Eduardo Marcos, Octavio Mendoza","submitted_at":"2018-04-03T20:58:47Z","abstract_excerpt":"We study the cokernel of the application given by the Cartan Matrix $C_\\Lambda$ of a finite dimensional $k$-algebra $\\Lambda.$ This produces a finitely generated abelian group, the Cartan group $G_\\Lambda,$ which is invariant under derived equivalences. We are interested in the case when $G_\\Lambda$ is finite. For a standardly stratified algebra, it is shown that this group is always finite and some interesting connections with the standard modules are found. As a consequence, it is got that $G_\\Lambda$ can be seen as a measure of how far is a standardly stratified algebra $\\Lambda$ to be quas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01168","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":"1804.01168","created_at":"2026-05-18T00:19:15.880271+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01168v1","created_at":"2026-05-18T00:19:15.880271+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01168","created_at":"2026-05-18T00:19:15.880271+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4VXWSQQHXWC","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4VXWSQQHXWCI7NJ","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4VXWSQQ","created_at":"2026-05-18T12:32:56.356000+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/V4VXWSQQHXWCI7NJCGP6OTTHXN","json":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN.json","graph_json":"https://pith.science/api/pith-number/V4VXWSQQHXWCI7NJCGP6OTTHXN/graph.json","events_json":"https://pith.science/api/pith-number/V4VXWSQQHXWCI7NJCGP6OTTHXN/events.json","paper":"https://pith.science/paper/V4VXWSQQ"},"agent_actions":{"view_html":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN","download_json":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN.json","view_paper":"https://pith.science/paper/V4VXWSQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01168&json=true","fetch_graph":"https://pith.science/api/pith-number/V4VXWSQQHXWCI7NJCGP6OTTHXN/graph.json","fetch_events":"https://pith.science/api/pith-number/V4VXWSQQHXWCI7NJCGP6OTTHXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN/action/storage_attestation","attest_author":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN/action/author_attestation","sign_citation":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN/action/citation_signature","submit_replication":"https://pith.science/pith/V4VXWSQQHXWCI7NJCGP6OTTHXN/action/replication_record"}},"created_at":"2026-05-18T00:19:15.880271+00:00","updated_at":"2026-05-18T00:19:15.880271+00:00"}