{"paper":{"title":"Boundary operator algebras for free uniform tree lattices","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Guyan Robertson","submitted_at":"2004-07-15T08:37:21Z","abstract_excerpt":"Let $X$ be a finite connected graph, each of whose vertices has degree at least three. The fundamental group $\\Gamma$ of $X$ is a free group and acts on the universal covering tree $\\Delta$ and on its boundary $\\partial \\Delta$, endowed with a natural topology and Borel measure. The crossed product $C^*$-algebra $C(\\partial \\Delta) \\rtimes \\Gamma$ depends only on the rank of $\\Gamma$ and is a Cuntz-Krieger algebra whose structure is explicitly determined. The crossed product von Neumann algebra does not possess this rigidity. If $X$ is homogeneous of degree $q+1$ then the von Neumann algebra $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407266","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"}