{"paper":{"title":"Smooth cohomology of $ C^* $-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Ahmad Shirinkalam, Massoud Amini","submitted_at":"2018-10-18T18:00:59Z","abstract_excerpt":"We define a notion of smooth cohomology for $ C^* $-algebras which admit a faithful trace. We show that if $ \\A\\subseteq B(\\h) $ is a $ C^* $-algebra with a faithful normal trace $ \\tau $ on the ultra-weak closure $ \\bar{\\A} $ of $ \\mathcal{A} $, and $ X $ is a normal dual operatorial $ \\bar{\\A}$-bimodule, then the first smooth cohomology $ \\mathcal{H}^1_{s}(\\mathcal{A},X) $ of $ \\mathcal{A} $ is equal to $ \\mathcal{H}^1(\\mathcal{A},X_{\\tau})$, where $ X_{\\tau} $ is a closed submodule of $ X $ consisting of smooth elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08216","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"}