{"paper":{"title":"Leibniz seminorms for \"Matrix algebras converge to the sphere\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MG"],"primary_cat":"math.OA","authors_text":"Marc A. Rieffel (U. C. Berkeley)","submitted_at":"2007-07-21T21:03:23Z","abstract_excerpt":"In an earlier paper of mine relating vector bundles and Gromov-Hausdorff distance for ordinary compact metric spaces, it was crucial that the Lipschitz seminorms from the metrics satisfy a strong Leibniz property. In the present paper, for the now non-commutative situation of matrix algebras converging to the sphere (or to other spaces) for quantum Gromov-Hausdorff distance, we show how to construct suitable seminorms that also satisfy the strong Leibniz property. This is in preparation for making precise certain statements in the literature of high-energy physics concerning \"vector bundles\" o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3229","kind":"arxiv","version":3},"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"}