{"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"}