کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6415164 | 1334953 | 2013 | 22 صفحه PDF | دانلود رایگان |
We study the Haagerup property for Câ-algebras. We first give new examples of Câ-algebras with the Haagerup property. A nuclear Câ-algebra with a faithful tracial state always has the Haagerup property, and the permanence of the Haagerup property for Câ-algebras is established. As a consequence, the class of all Câ-algebras with the Haagerup property turns out to be quite large. We then apply Popaʼs results and show the Câ-algebras with property (T) have a certain rigidity property. Unlike the case of von Neumann algebras, for the reduced group Câ-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 Câ-algebras of the (non-amenable) affine groups of the affine planes have a rigidity property.
Journal: Journal of Functional Analysis - Volume 265, Issue 8, 15 October 2013, Pages 1778-1799