{"paper":{"title":"Module and Hochschild cohomology of certain semigroup algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Pourabbas, A. Shirinkalam, M. Amini","submitted_at":"2014-12-16T12:35:46Z","abstract_excerpt":"We study the relation between module and Hochschild cohomology groups of Banach algebras with a compatible module structure. More precisely, we show that for every commutative Banach\n  $ \\mathcal{A} $-$ \\mathfrak{A}$-bimodule $ X $ and every $ k \\in \\mathbb{N}$, the seminormed spaces\n  $ \\mathcal{H}^{k}_{\\mathfrak{A}} (\\mathcal{A},X^*)$ and $ \\mathcal{H}^k (\\frac{\\mathcal{A}}{J}, X^*) $ are isomorphic, where $ J $ is the closed ideal of $ \\mathcal{A} $ generated by the elements of the form $ a (\\alpha \\cdot b)-(a\\cdot \\alpha)b$ with $ a,b \\in \\mathcal{A} $ and $\\alpha \\in \\mathfrak{A}. $\n  As "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4978","kind":"arxiv","version":2},"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"}