{"paper":{"title":"Splitting Algebras II: The Cohomology Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Brad Shelton","submitted_at":"2012-08-10T15:14:45Z","abstract_excerpt":"Gelfand, Retakh, Serconek and Wilson, in \\cite{GRSW}, defined a graded algebra $A_\\Gamma$ attached to any finite ranked poset $\\Gamma$ - a generalization of the universal algebra of pseudo-roots of noncommutative polynomials. This algebra has since come to be known as the splitting algebra of $\\Gamma$. The splitting algebra has a secondary filtration related to the rank function on the poset and the associated graded algebra is denoted here by $A'_\\Gamma$. We calculate the cohomology algebra (and coalgebra) of $A'_\\Gamma$ explicitly. As a corollary to this calculation we have a proof that $A'_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2202","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"}