{"paper":{"title":"Asymptotic K-theory for groups acting on $\\tildeA_2$ buildings","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Guyan Robertson, Tim Steger","submitted_at":"2000-11-23T03:35:52Z","abstract_excerpt":"Let $\\Gamma$ be a torsion free lattice in $G=\\PGL(3,{{\\mathbb F}})$ where ${{\\mathbb F}}$ is a nonarchimedean local field. Then $\\Gamma$ acts freely on the affine Bruhat-Tits building ${\\mathcal B}$ of $G$ and there is an induced action on the boundary $\\Omega$ of ${\\mathcal B}$. The crossed product $C^*$-algebra ${\\mathcal A}(\\Gamma)=C(\\Omega) \\rtimes \\Gamma$ depends only on $\\Gamma$ and is classified by its K-theory. This article shows how to compute the K-theory of ${\\mathcal A}(\\Gamma)$ and of the larger class of rank two Cuntz-Krieger algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011191","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"}