{"paper":{"title":"Noncommutative differential operators, Sobolev spaces and the centre of a category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Edwin Beggs, Tomasz Brzezinski","submitted_at":"2011-08-25T09:31:36Z","abstract_excerpt":"We consider differential operators over a noncommutative algebra $A$ generated by vector fields. These are shown to form a unital associative algebra of differential operators, and act on $A$-modules $E$ with covariant derivative. We use the repeated differentials given in the paper to give a definition of noncommutative Sobolev space for modules with connection and Hermitian inner product. The tensor algebra of vector fields, with a modified bimodule structure and a bimodule connection, is shown to lie in the centre of the bimodule connection category ${}_A\\mathcal{E}_A$, and in fact to be an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5047","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"}