{"paper":{"title":"KMS states on the operator algebras of reducible higher-rank graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Astrid an Huef, Iain Raeburn, Sooran Kang","submitted_at":"2016-10-21T02:15:24Z","abstract_excerpt":"We study the equilibrium or KMS states of the Toeplitz C*-algebra of a finite higher-rank graph which is reducible. The Toeplitz algebra carries a gauge action of a higher-dimensional torus, and a dynamics arises by choosing an embedding of the real numbers in the torus. Here we use an embedding which leads to a dynamics which has previously been identified as \"preferred\", and we scale the dynamics so that 1 is a critical inverse temperature. As with 1-graphs, we study the strongly connected components of the vertices of the graph. The behaviour of the KMS states depends on both the graphical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06648","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"}