{"paper":{"title":"C*-algebras of Boolean inverse monoids - traces and invariant means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.OA","authors_text":"Charles Starling","submitted_at":"2016-05-17T14:36:54Z","abstract_excerpt":"To a Boolean inverse monoid $S$ we associate a universal C*-algebra $C_B^*(S)$ and show that it is equal to Exel's tight C*-algebra of $S$. We then show that any invariant mean on $S$ (in the sense of Kudryavtseva, Lawson, Lenz and Resende) gives rise to a trace on $C_B^*(S)$, and vice-versa, under a condition on $S$ equivalent to the underlying groupoid being Hausdorff. Under certain mild conditions, the space of traces of $C_B^*(S)$ is shown to be isomorphic to the space of invariant means of $S$. We then use many known results about traces of C*-algebras to draw conclusions about invariant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05189","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"}