{"paper":{"title":"Local Deformation of Matrix Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Fredy Vides","submitted_at":"2016-08-30T17:10:02Z","abstract_excerpt":"In this document we study some local deformation properties of matrix representations of the universal C$^*$-algebras denoted by $\\mathbb{I}^{m}_\\varepsilon[p_1,\\ldots,p_m]$ and $\\mathbb{S}^{m-1}_\\varepsilon[p_1,\\ldots,p_m]$, and that we call {\\bf Semi-Soft Cubes} and {\\bf Semi-Soft Spheres} respectively.\n  We will use some C$^*$-algebraic technology to study the local deformation properties of matrix words in particular representations of Semi-Soft Cubes and Spheres, we will then use these results to study the local deformation properties of generic matrix equations on words.\n  Some geometric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08562","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"}