{"paper":{"title":"Computational explorations of the Thompson group T for the amenability problem of F","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"M. Ramirez-Solano, S. Haagerup, U. Haagerup","submitted_at":"2017-04-29T14:38:23Z","abstract_excerpt":"It is a long standing open problem whether the Thompson group $F$ is an amenable group. In this paper we show that if $A$, $B$, $C$ denote the standard generators of Thompson group $T$ and $D:=C B A^{-1}$ then $$\\sqrt2+\\sqrt3\\,<\\,\\frac1{\\sqrt{12}}||(I+C+C^2)(I+D+D^2+D^3)||\\,\\le\\, 2+\\sqrt2.$$ Moreover, the upper bound is attained if the Thompson group $F$ is amenable. Here, the norm of an element in the group ring $\\mathbb{C} T$ is computed in $B(\\ell^2(T))$ via the regular representation of $T$. Using the \"cyclic reduced\" numbers $\\tau(((C+C^2)(D+D^2+D^3))^n)$, $n\\in\\mathbb{N}$, and some metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00198","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"}