{"paper":{"title":"Generalized gauge actions on $k$-graph $C^*$-algebras: KMS states and Hausdorff structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OA","authors_text":"Carla Farsi, Elizabeth Gillaspy, Judith A. Packer, Nadia S. Larsen","submitted_at":"2018-07-23T15:13:36Z","abstract_excerpt":"For a finite, strongly connected $k$-graph $\\Lambda$, an Huef, Laca, Raeburn and Sims studied the KMS states associated to the preferred dynamics of the $k$-graph $C^*$-algebra $C^*(\\Lambda)$. They found that these KMS states are determined by the periodicity of $\\Lambda$ and a certain Borel probability measure $M$ on the infinite path space $\\Lambda^\\infty$ of $\\Lambda$. Here we consider different dynamics on $C^*(\\Lambda)$, which arise from a functor $y: \\Lambda \\to \\mathbb{R}_+$ and were first proposed by McNamara in his thesis. We show that the KMS states associated to McNamara's dynamics "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08665","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"}