{"paper":{"title":"On $C^*$-algebras of exponential solvable Lie groups and their real ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.OA","authors_text":"Daniel Beltita, Ingrid Beltita","submitted_at":"2015-11-17T20:17:22Z","abstract_excerpt":"For any solvable Lie group whose exponential map $\\exp_G\\colon{\\mathfrak g}\\to G$ is bijective, we prove that the real rank of $C^*(G)$ is equal to $\\dim({\\mathfrak g}/[{\\mathfrak g},{\\mathfrak g}])$. We also indicate a proof of a similar formula for the stable rank of $C^*(G)$, as well as some estimates on the ideal generated by the projections in $C^*(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05533","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"}