{"paper":{"title":"Symmetries of the KMS simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Johannes Christensen","submitted_at":"2017-10-12T08:49:04Z","abstract_excerpt":"A continuous groupoid homomorphism $c$ on a locally compact second countable Hausdorff \\'etale groupoid $\\mathcal{G}$ gives rise to a $C^{*}$-dynamical system in which every $\\beta$-KMS state can be associated to a $e^{-\\beta c}$-quasi-invariant measure $\\mu$ on $\\mathcal{G}^{(0)}$. Letting $\\Delta_{\\mu}$ denote the set of KMS states associated to such a $\\mu$, we will prove that $\\Delta_{\\mu}$ is a simplex for a large class of groupoids, and we will show that there is an abelian group that acts transitively and freely on the extremal points of $\\Delta_{\\mu}$. This group can be described using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04412","kind":"arxiv","version":2},"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"}