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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.0428","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-02T00:17:56Z","cross_cats_sorted":[],"title_canon_sha256":"cb5d40b0ce44caf74a2b228c5f33143393ee2f9678af592e2338d0e342c0800a","abstract_canon_sha256":"c37be57d5bed2281de84c523f10470456819fd59fe32a68e5b789946a46601d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:55.091448Z","signature_b64":"7btAzHNsNDMC+pstYWHxQcB+x/kQfNlwOz96gEd51FEdqSH8VuvBvNZpjuXh2Jm5RfLhCR+CHiP80JCqoHqmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"325e297a5434aaac88f84efe0c977e8442a663857c0b52aefb5bef26518e9b72","last_reissued_at":"2026-05-18T02:28:55.091068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:55.091068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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