{"paper":{"title":"Full groups of Cuntz-Krieger algebras and Higman-Thompson groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Hiroki Matui, Kengo Matsumoto","submitted_at":"2014-09-17T00:27:11Z","abstract_excerpt":"In this paper, we will study presentations of the continuous full group $\\Gamma_A$ of a one-sided topological Markov shift $(X_A,\\sigma_A)$ for an irreducible matrix $A$ with entries in $\\{0,1\\}$ as a generalization of Higman-Thompson groups $V_N, 1<N \\in {\\mathbb{N}}$. We will show that the group $\\Gamma_A$ can be represented as a group $\\Gamma_A^{\\operatorname{tab}}$ of matrices, called $A$-adic tables, with entries in admissible words of the shift space $X_A$, and a group $\\Gamma_A^{\\operatorname{PL}}$ of right continuous piecewise linear functions, called $A$-adic PL functions, on $[0,1]$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4838","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"}