{"paper":{"title":"On the Ext Ring of Koszul Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Adrian Manea","submitted_at":"2015-06-01T08:37:12Z","abstract_excerpt":"The aim of this article is to study the Ext ring associated to a Koszul $R$-ring and to use it to provide further characterisations of the former. As such, for $R$ being a semisimple ring and $A$ a graded Koszul $R$-ring, we will prove that there is an isomorphism of DG rings between $\\mathcal{E}(A):=\\mathrm{Ext}^\\bullet_A(R,R)$ and $^{\\ast-\\text{gr}}\\mathrm{T}(A) \\simeq \\mathrm{E}(^{\\ast-\\text{gr}\\!} A)$. Also, the Ext $R$-ring will prove to be isomorphic to the shriek ring of the left graded dual of $A$, namely $\\mathcal{E}(A) \\simeq (^{\\ast-\\text{gr}\\!} A)^!$. As an application, these isomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00387","kind":"arxiv","version":3},"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"}