{"paper":{"title":"On the K-theory of boundary $C^*$-algebras of $\\widetilde A_2$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.KT","authors_text":"Guyan Robertson, Oliver King","submitted_at":"2011-04-22T10:21:43Z","abstract_excerpt":"Let $\\Gamma$ be an $\\widetilde A_2$ subgroup of $\\PGL_3(\\mathbb K)$, where $\\mathbb K$ is a local field with residue field of order $q$. The module of coinvariants $C(\\mathbb P^2_{\\mathbb K},\\mathbb Z)_{\\Gamma}$ is shown to be finite, where $\\mathbb P^2_{\\mathbb K}$ is the projective plane over $\\mathbb K$. If the group $\\Gamma$ is of Tits type and if $q \\not\\equiv 1 \\pmod {3}$ then the exact value of the order of the class $[I]_{K_0}$ in the K-theory of the (full) crossed product $C^*$-algebra $C(\\Omega)\\rtimes\\Gamma$ is determined, where $\\Omega$ is the Furstenberg boundary of $\\PGL_3(\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4416","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"}