{"paper":{"title":"On some cocycles which represent the Dixmier-Douady class in simplicial de Rham complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Naoya Suzuki","submitted_at":"2013-10-17T01:36:30Z","abstract_excerpt":"When a Lie group $G$ has a central $U(1)$-extension, there is a cocycle in the simplicial de Rham complex $\\Omega^3(NG)$ which represents the Dixmier-Douady class. Mickelsson and Brylinski, McLaughlin constructed a central $U(1)$-extension $\\widehat{LSU(2)} \\rightarrow LSU(2)$ whose Dixmier-Douady class in $\\Omega^3(NLSU(2))$ is a kind of transgression of the second Chern class.\n  In this paper, we consider the case of unitary group and construct a central $U(1)$-extension of $LU(2)$. After that we construct also a cocycle in a certain triple complex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4559","kind":"arxiv","version":17},"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"}