{"paper":{"title":"Torsion in K-theory for boundary actions on affine buildings of type $\\tA_n$","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Guyan Robertson","submitted_at":"2000-11-23T03:58:02Z","abstract_excerpt":"Let $\\Gamma$ be a torsion free lattice in $G = \\PGL(n+1,\\FF)$, where $n\\ge 1$ and $\\FF$ is a non-archimedean local field. Then $\\Gamma$ acts on the Furstenberg boundary $G/P$, where $P$ is a minimal parabolic subgroup of $G$. The identity element $\\id$ in the crossed product $C^*$-algebra $C(G/P)\\rtimes \\Gamma$ generates a class $[\\id]$ in the $K_0$ group of $C(G/P)\\rtimes \\Gamma$. It is shown that $[\\id]$ is a torsion element of $K_0$ and there is an explicit bound for the order of $[\\id]$. The result is proved more generally for groups acting on affine buildings of type $\\tA_n$. For $n=1, 2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011192","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"}