{"paper":{"title":"Weakly Cohen-Macaulay posets and a class of finite-dimensional graded quadratic algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Tyler Kloefkorn","submitted_at":"2016-03-30T04:51:42Z","abstract_excerpt":"To a finite ranked poset $\\Gamma$ we associate a finite-dimensional graded quadratic algebra $R_\\Gamma$. Assuming $\\Gamma$ satisfies a combinatorial condition known as uniform, $R_{\\Gamma}$ is related to a well-known algebra, the splitting algebra $A_{\\Gamma}$. First introduced by Gelfand, Retakh, Serconek, and Wilson, splitting algebras originated from the problem of factoring non-commuting polynomials. Given a finite ranked poset $\\Gamma$, we ask: Is $R_{\\Gamma}$ Koszul? The Koszulity of $R_{\\Gamma}$ is related to a combinatorial topology property of $\\Gamma$ called Cohen-Macaulay. Kloefkorn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09038","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"}