Property Gamma and inner amenability
Property Gamma and inner amenability
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属性伽玛和内在的顺从性
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Erik Christensen
中科院分区：
文献类型：
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作者：
K. Olesen;Erik Christensen
本课题研究群的内在顺从性与其关联群的性质Γ之间的关系。证明了具有无穷共轭类的群是内顺从的，如果它的伴随群von Neumann代数具有性质Γ.介绍了冯·诺依曼代数的群和张量积的构造方法，包括冯·诺依曼代数的无穷张量积。最后，我们给出了一个具有无穷共轭类的内顺从群的例子，它的伴随群von Neumann代数不具有性质Γ，从而证明了第一部分所证明结果的匡威蕴涵是不成立的.
This project contains an investigation of the relationship between inner amenability of a group and property Γ of its associated group von Neumann algebra. We prove that a group with infinite conjugacy classes is inner amenable if its associated group von Neumann algebra has property Γ. Some theory concerning ways of constructing groups and tensor products of von Neumann algebras is covered, including infinite tensor products of von Neumann algebras. Lastly we give an example of an inner amenable group with infinite conjugacy classes whose associated group von Neumann algebra does not have property Γ; thus showing that the converse implication to the result proved in the first part is not true.