{"paper":{"title":"$C^*$--algebras arising from group actions on the boundary of a triangle building","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guyan Robertson, Tim Steger","submitted_at":"2013-02-24T16:26:32Z","abstract_excerpt":"A subgroup of an amenable group is amenable. The $C^*$-algebra version of this fact is false. This was first proved by M.-D. Choi who proved that the non-nuclear $C^*$-algebra $C^*_r(\\ZZ_2*\\ZZ_3)$ is a subalgebra of the nuclear Cuntz algebra ${\\cal O}_2$. A. Connes provided another example, based on a crossed product construction. More recently J. Spielberg [23] showed that these examples were essentially the same. In fact he proved that certain of the $C^*$-algebras studied by J. Cuntz and W. Krieger [10] can be constructed naturally as crossed product algebras. For example if the group $\\Gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5920","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"}