{"paper":{"title":"Productive elements in group cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ergun Yalcin","submitted_at":"2011-01-20T07:54:20Z","abstract_excerpt":"Let $G$ be a finite group and $k$ be a field of characteristic $p>0$. A cohomology class $\\zeta \\in H^n(G,k)$ is called productive if it annihilates $\\Ext^*_{kG}(L_{\\zeta},L_{\\zeta})$. We consider the chain complex $\\bPz$ of projective $kG$-modules which has the homology of an $(n-1)$-sphere and whose $k$-invariant is $\\zeta$ under a certain polarization. We show that $\\zeta$ is productive if and only if there is a chain map $\\Delta: \\bPz \\to \\bPz \\otimes \\bPz$ such that $(\\id \\otimes \\epsilon)\\Delta\\simeq \\id$ and $(\\epsilon \\otimes \\id)\\Delta \\simeq \\id$. Using the Postnikov decomposition of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3834","kind":"arxiv","version":2},"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"}