{"paper":{"title":"Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guyan Robertson, Tim Steger","submitted_at":"2013-02-22T13:56:39Z","abstract_excerpt":"To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In particular, it is simple, purely infinite and nuclear. We study an example: if $\\G$ is a group acting freely on the vertices of an $\\wt A_2$ building, with finitely many orbits, and if $\\Omega$ is the boundary of that building, then $C(\\Om)\\rtimes \\G$ is the algebra associated to a certain two dimensional subshift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5593","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"}