{"paper":{"title":"Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Enrique Pardo, Ruy Exel","submitted_at":"2014-09-03T14:36:33Z","abstract_excerpt":"Given a graph $E$, an action of a group $G$ on $E$, and a $G$-valued cocycle $\\phi$ on the edges of $E$, we define a C*-algebra denoted ${\\cal O}_{G,E}$, which is shown to be isomorphic to the tight C*-algebra associated to a certain inverse semigroup $S_{G,E}$ built naturally from the triple $(G,E,\\phi)$. As a tight C*-algebra, ${\\cal O}_{G,E}$ is also isomorphic to the full C*-algebra of a naturally occurring groupoid ${\\cal G}_{tight}(S_{G,E})$. We then study the relationship between properties of the action, of the groupoid and of the C*-algebra, with an emphasis on situations in which ${\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1107","kind":"arxiv","version":3},"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"}