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If we further assume the diagonal actions $\\sigma^2, \\sigma^4$ are $\\mathbb{T}$-cocycle superrigid and $H^2(G, \\widehat{X})$ is torsion free as an abelian group, then the above also holds true for $n=2$. Applying it for principal algebraic actions when $n=1$, we show that $H^2(G,\\mathbb{Z}G)$ is torsion free as an abeli"},"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":"1509.08278","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2015-09-28T11:25:11Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"77cb6c808412f9b497e8ecf85b74b1d74021cb3a0cd48c2127677b4d89c3a67d","abstract_canon_sha256":"f6ae37b4d20279b0a3e2caf6ba66aa27a2f215fbf9e8984d740e52ec820efa24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:09.596552Z","signature_b64":"SfoM5kZQ998nT+7rgbB+DbGUwtk3aJ/zbIfV4wmKcc15BqEm8Wn6ofxasMAjiW8usq31bG3R3wmfAfIE01/IBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"994f9b23be65a72b7a44be9c9acb038a286efc208c4b0f51b45a7a5635e9f93f","last_reissued_at":"2026-05-18T01:13:09.596164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:09.596164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark on $\\mathbb{T}$-valued cohomology groups of algebraic group actions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Yongle Jiang","submitted_at":"2015-09-28T11:25:11Z","abstract_excerpt":"We prove that for a weakly mixing algebraic action $\\sigma: G\\curvearrowright(X,\\nu)$, the $n$-cohomology group $H^n(G\\curvearrowright X; \\mathbb{T})$, after quotienting out the natural subgroup $H^n(G,\\mathbb{T})$, contains $H^n(G,\\widehat{X})$ as a natural subgroup for $n=1$. 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