{"paper":{"title":"The extension class and KMS states for Cuntz--Pimsner algebras of some bi-Hilbertian bimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Adam Rennie, Aidan Sims, David Robertson","submitted_at":"2015-01-22T01:26:10Z","abstract_excerpt":"For bi-Hilbertian $A$-bimodules, in the sense of Kajiwara--Pinzari--Watatani, we construct a Kasparov module representing the extension class defining the Cuntz--Pimsner algebra. The construction utilises a singular expectation which is defined using the $C^*$-module version of the Jones index for bi-Hilbertian bimodules. The Jones index data also determines a novel quasi-free dynamics and KMS states on these Cuntz--Pimsner algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05363","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"}