2012/12/31 by Yuhei Suzuki · 19 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Affine transformation #Chemistry #Group (periodic table) #Mathematics #Noncommutative and Quantum Gravity Theories #Property (philosophy) #Pure mathematics #Rigidity (electromagnetism) #Von Neumann architecture #math.OA
paper · pdf · doi:10.1016/j.jfa.2013.06.007
published in Journal of Functional Analysis 265(8), 1778-1799 (Elsevier BV) · This is the final version. 22pages, no figures
openalex publication_date 2013/06/13 · arxiv created 2013/07/23 · arxiv updated 2013/07/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the Haagerup property for C*-algebras. We first give new examples of C*-algebras with the Haagerup property. A nuclear C*-algebra with a faithful tracial state always has the Haagerup property, and the permanence of the Haagerup property for C*-algebras is established. As a consequence, the class of all C*-algebras with the Haagerup property turns out to be quite large. We then apply Popa's results and show the C*-algebras with property (T) have a certain rigidity property. Unlike the case of von Neumann algebras, for the reduced group C*-algebras of groups with relative property (T), the rigidity property strongly fails in general. Nevertheless, for some groups without nontrivial property (T) subgroups, we show a rigidity property in some cases. As examples, we prove the reduced group C*-algebras of the (non-amenable) affine groups of the affine planes have a rigidity property.