{"paper":{"title":"Cohomology of Lie semidirect products and poset algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Murray Gerstenhaber, Vincent E. Coll Jr.","submitted_at":"2014-07-02T00:17:56Z","abstract_excerpt":"When $\\mathfrak h$ is a toral subalgebra of a Lie algebra $\\mathfrak g$ over a field $\\mathbf k$, and $M$ a $\\mathfrak g$-module on which $\\mathfrak h$ also acts torally, the Hochschild-Serre filtration of the Chevalley-Eilenberg cochain complex admits a stronger form than for an arbitrary subalgebra. For a semidirect product $\\mathfrak g = \\mathfrak h \\ltimes \\mathfrak k$ with $\\mathfrak h$ toral one has $H^*(\\mathfrak g, M) \\cong \\bigwedge\\mathfrak h^{\\vee} \\bigotimes H^*(\\mathfrak k,M)^{\\mathfrak h} = H^*(\\mathfrak h, \\mathbf k)\\bigotimes H^*(\\mathfrak k,M)^{\\mathfrak h}$, and for a Lie pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0428","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"}