Purely infinite C*-algebras from boundary actions of discrete groups.
Purely infinite C*-algebras from boundary actions of discrete groups.
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来自离散群边界作用的纯无限 C* 代数。
DOI：
10.1515/crll.1996.480.125
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Marcelo Laca
中科院分区：
文献类型：
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作者：
J. Spielberg;Marcelo Laca
有各种动力系统产生简单C*-代数的例子，其中双曲性或其弱化形式排除了迹的存在。在这些情况下，人们自然会认为C*-代数是纯无限的。E.Kirchberg和C.Phillips最近在简单纯无限核C*代数的KK等价分类方面所做的工作极大地提高了证明这些例子是纯无限的重要性。例如，作用在上半平面边界上的模群和作用于二进螺线管上的位移，具有非常有趣的相似之处。一旦相应的C*-代数被证明是纯无限的，就可以通过计算它们的K-理论来得出它们是强Morita等价的结论(应用15)。
There are various examples of dynamical Systems giving rise to simple C*-algebras, in which hyperbolicity, or a weakened form thereof, precludes the existence of a trace. In these situations one naturally expects the C*-algebras to be purely infinite. Recent work of E. Kirchberg and C. Phillips on the classification of simple purely infinite nuclear C*algebras by KK-equivalence has dramatically heightened the importance of proving that these examples are purely infinite. For example, the modular group acting on the boundary of the upper half plane, and the shift on the 2-adic solenoid, have very intriguing similarities. Once the corresponding C*-algebras are shown to be purely infinite, one can conclude that they are strongly Morita equivalent by Computing their K-theory (Application 15).