{"paper":{"title":"Low dimensional cohomology of general conformal algebras $gc_N$","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Yucai Su","submitted_at":"2004-02-26T02:58:57Z","abstract_excerpt":"We compute the low dimensional cohomologies $\\tilde H^q(gc_N,C)$, $H^q(gc_N,\\C)$ of the infinite rank general Lie conformal algebras $gc_N$ with trivial coefficients for $q\\le3, N=1$ or $q\\le2, N\\ge2$. We also prove that the cohomology of $gc_N$ with coefficients in its natural module is trivial, i.e., $H^*(gc_N,\\C[\\ptl]^N)=0$; thus partially solve an open problem of Bakalov-Kac-Voronov in [{\\it Comm. Math. Phys.,} {\\bf200} (1999), 561-598]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402421","kind":"arxiv","version":1},"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"}