C* 代数的几何实现与K-理论分解
Geometric realization and K-theoretic decomposition of C*-algebras
摘要：
设A是可分C* 代数，G * 是K *（A）的（分次）子群.则存在自然短正合序列0 \to G_* \to K_*（A）\to K_*（A）/G_* \to 0.在这篇注记中，我们演示了如何在C* 代数的水平上几何地实现这个序列。因此，我们在理论上将A分解为0 \to A \otimes \Cal K \to A_f \to SA_t \to 0其中K_*（A_t）是K_*（A）的挠子群，K_*（A_f）是它的无挠商.然后我们进一步分解A_t：它与\oplus_p A_p是KK-等价的，其中K_*（A_p）是K_*（A）的挠子群的p-准素子群.然后我们应用这个实现来研究Kasparov群K^*（A）和相关的对象。
英文摘要：
Suppose that A is a separable C*-algebra and that G_* is a (graded) subgroup of K_*(A). Then there is a natural short exact sequence 0 \to G_* \to K_*(A) \to K_*(A)/G_* \to 0. In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as 0 \to A\otimes \Cal K \to A_f \to SA_t \to 0 where K_*(A_t) is the torsion subgroup of K_*(A) and K_*(A_f) is its torsionfree quotient. Then we further decompose A_t : it is KK-equivalent to \oplus_p A_p where K_*(A_p) is the p-primary subgroup of the torsion subgroup of K_*(A). We then apply this realization to study the Kasparov group K^*(A) and related objects.
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