K-theoretic amenability for discrete groups.
K-theoretic amenability for discrete groups.
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离散群的 K 理论适用性。
DOI：
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发表时间：
1983
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通讯作者：
J. Cuntz
中科院分区：
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作者：
J. Cuntz
本文工作的出发点是Pimsner和Vojculescu [18]计算n个生成元上自由群Fn的约化C*-代数的K-群（这也是一个推论，证明了Kadison的旧猜想，见Powers [19]，即这个C*-代数除了0和1之外不包含投影）。他们的论证的复杂性与作者在[7]中对Fn的füll C*-代数的相应群的几乎平凡而相当正式的计算形成了鲜明的对比。此外，Pimsner-Voiculescu的方法不适用于Δ T-同调和KK群，因为它依赖于长正合序列，而对于非核C*-代数，这在AT-同调中是不可用的。因此，从füll C*-代数的结果推导出约化C*-代数的结果似乎是可取的。此外，很明显，这种尝试的正确框架将是卡斯帕罗夫的理论。
The starting point for the work in this paper was the computation, by Pimsner and Vojculescu [18], of the K-groups for the reduced C*-algebra of the free group Fn on n generators (which also, äs a corollary, proved the old conjecture of Kadison, see Powers [19], that this C*-algebra contains no projections except 0 and 1). The intricacy of their argument is in striking contrast to the nearly trivial and rather formal computation of the corresponding groups for the füll C*-algebra of Fn by the author in [7]. Also, the method of Pimsner-Voiculescu does not work for the ÄT-homology and KKgroups, since it depends on the long exact sequence which, for non-nuclear C*-algebras, is not available in AT-homology. It seemed therefore desirable to deduce the result for the reduced C*-algebra from the result for the füll C*-algebra. It was, moreover, obvious that the right frame for such an attempt would be the , -theory of Kasparov.