{"paper":{"title":"Bergman's Centralizer Theorem and quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alexei Kanel Belov, Farrokh Razavinia, Wenchao Zhang","submitted_at":"2017-08-16T08:30:25Z","abstract_excerpt":"We prove Bergman's theorem on centralizers by using generic matrices and Kontsevich's quantization method. For any field $\\textbf{k} $ of positive characteristics, set $A=\\textbf{k} \\langle x_1,\\dots,x_s\\rangle$ be a free associative algebra, then any centralizer $\\mathcal{C}(f)$ of nontrivial element $f\\in A\\backslash \\textbf{k}$ is a ring of polynomials on a single variable. We also prove that there is no commutative subalgebra with transcendent degree $\\geq 2$ of $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04802","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"}