Property (T), property (F) and residual finiteness for discrete quantum groups
Property (T), property (F) and residual finiteness for discrete quantum groups
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DOI：
10.4171/jncg/373
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发表时间：
2017-12
影响因子：
0.9
通讯作者：
Angshuman Bhattacharya;Michael Brannan;A. Chirvasitu;Shuzhou Wang
中科院分区：
文献类型：
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作者：
Angshuman Bhattacharya;Michael Brannan;A. Chirvasitu;Shuzhou Wang
我们研究了离散量子群的各种刚性和柔软性之间的联系。在引入剩余有限性的概念后，我们证明了它蕴含着离散量子群的Kirchberg分解性质。我们还证明了类似的Kirchberg定理，反之，分解性质和性质(T)共同蕴含剩余有限性。我们还将这些结果应用于通过双微积构造得到的某些类离散量子群，并研究了这些性质(因式分解、剩余有限性、性质(T))在离散量子群扩张下的保持。
We investigate connections between various rigidity and softness properties for discrete quantum groups. After introducing a notion of residual finiteness, we show that it implies the Kirchberg factorization property for the discrete quantum group in question. We also prove the analogue of Kirchberg's theorem, to the effect that conversely, the factorization property and property (T) jointly imply residual finiteness. We also apply these results to certain classes of discrete quantum groups obtained by means of bicrossed product constructions and study the preservation of the properties (factorization, residual finiteness, property (T)) under extensions of discrete quantum groups.