2014/10/31 by Yuhei Suzuki
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Combinatorics #Exact sequence #Group (periodic table) #Group algebra #Intersection (aeronautics) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Separable space #Von Neumann algebra #Von Neumann architecture #math.GR #math.OA #msc:46L05
paper · pdf · doi:10.1353/ajm.2017.0018
published as The American Journal of Mathematics 139 (2017), 681--705 · 22 pages. More detailed proofs. No substantial change. To appear in Amer. J. Math. Expanded version of arXiv:1406.2740
arxiv created 2016/01/11 · openalex publication_date 2017/01/01 · arxiv updated 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that for every exact discrete group Γ, there is an intermediate \rm C^∗-algebra between the reduced group \rm C^∗-algebra and the intersection of the group von Neumann algebra and the uniform Roe algebra which is realized as the intersection of a decreasing sequence of isomorphs of the Cuntz algebra \cal O2. In particular, when Γ has the AP (approximation property), the reduced group \rm C^∗-algebra is realized in this way. We also study extensions of the reduced free group \rm C^∗-algebras and show that any exact absorbing or unital absorbing extension of it by any stable separable nuclear \rm C^∗-algebra is realized in this way.