{"paper":{"title":"Endomorphisms of the Cuntz Algebras and the Thompson Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Jeong Hee Hong, Sel\\c{c}uk Barlak, Wojciech Szymanski","submitted_at":"2017-03-20T15:23:50Z","abstract_excerpt":"We investigate the relationship between endomorphisms of the Cuntz algebra ${\\mathcal O}_2$ and endomorphisms of the Thompson groups $F$, $T$ and $V$ represented inside the unitary group of ${\\mathcal O}_2$. For an endomorphism $\\lambda_u$ of ${\\mathcal O}_2$, we show that $\\lambda_u(V)\\subseteq V$ if and only if $u\\in V$. If $\\lambda_u$ is an automorphism of ${\\mathcal O}_2$ then $u\\in V$ is equivalent to $\\lambda_u(F)\\subseteq V$. Our investigations are facilitated by introduction of the concept of modestly scaling endomorphism of ${\\mathcal O}_n$, whose properties and examples are investiga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06798","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"}