On the topology of the Kasparov groups and its applications
On the topology of the Kasparov groups and its applications
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卡斯帕罗夫群的拓扑结构及其应用
DOI：
10.1016/j.jfa.2005.02.015
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发表时间：
2004
影响因子：
1.7
通讯作者：
M. Dadarlat
中科院分区：
文献类型：
--
作者：
M. Dadarlat
本文建立了*-同态的稳定近似酉等价与kk群拓扑之间的直接联系，完全避免了C -代数的可拓理论，也不需要核假设。为此，我们证明了Kasparov群上的拓扑可以用Cuntz对的近似幺正等价来定义，并且该拓扑与Pimsner拓扑和Brown-Salinas拓扑都是一致的。研究了广义Rørdam群KL(A，B)=KK(A，B)/0¯，证明了一个可分离精确剩余有限维C*-代数满足KK理论中的普适系数定理，则它嵌入到2∞型UHF代数中。特别地，对于第二可数可调局部紧极大概周期群的C*-代数存在这样的嵌入。
In this paper we establish a direct connection between stable approximate unitary equivalence for *-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this topology coincides with both Pimsner's topology and the Brown–Salinas topology. We study the generalized Rørdam group KL(A,B)=KK(A,B)/0¯, and prove that if a separable exact residually finite dimensional C*-algebra satisfies the universal coefficient theorem in KK-theory, then it embeds in the UHF algebra of type 2∞. In particular such an embedding exists for the C*-algebra of a second countable amenable locally compact maximally almost periodic group.