Correction to: ‘The UCT, the Milnor Sequence, and a Canonical Decomposition of the Kasparov Groups’
Correction to: ‘The UCT, the Milnor Sequence, and a Canonical Decomposition of the Kasparov Groups’
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更正：“UCT、米尔诺数列和卡斯帕罗夫群的规范分解”
DOI：
10.1023/a:1007736102864
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Claude L. Schochet
中科院分区：
文献类型：
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作者：
Claude L. Schochet
设A是Bootstrap范畴N中的一个C-代数，其KKfiltration为A0 <$→ A1 <$→ A2 <$→。. . B是具有可数个近似单位的C-代数。然后分次Kasparov群KK <$（A，B）由泛系数定理0 → Ext Z（K <$（A），K <$（B））→ KK <$（A，B）→ HomZ（K <$（A），K <$（B））→ 0和Milnor lim <$−序列0 → lim <$− KK <$（Ai，B）−→ KK <$（A，B）−→ lim <$− KK <$（Ai，B）→ 0描述。证明了这两种描述是密切相关的，并且KK_n（A，B）不自然地分解为项的直和
Suppose that A is a C∗-algebra in the bootstrap category N with KKfiltration A0 ↪→ A1 ↪→ A2 ↪→ . . . and B is a C∗-algebra with a countable approximate unit. Then the graded Kasparov group KK∗(A, B) is described both by the Universal Coefficient Theorem 0 → Ext Z (K∗(A), K∗(B)) → KK∗(A, B) → HomZ(K∗(A), K∗(B)) → 0 and by the Milnor lim ←− sequence 0 → lim ←− KK∗(Ai, B) −→ KK∗(A, B) −→ lim ←− KK∗(Ai,B) → 0. It is demonstrated that these two descriptions are closely related and that KK∗(A, B) decomposes unnaturally as the direct sum of the term