Real C*-Algebras, United KK-Theory, and the Universal Coefficient Theorem
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- 作者：Jeffrey L. Boersema
- 关键词：K ; theory ; real C* ; algebras ; Universal Coefficient Theorem
- 刊名：K-Theory
- 出版时间：October 2004
- 出版年：2004
- 期刊代码：23_09203036
- 类别：eco
- 卷：33
- 期：2
- 页码：107-149
- 数据来源：sp
摘要
We define united KK-theory for real C*-algebras A and B such that A is separable and B is \mathbb R{\mathbb R} , B) = KCRT(B). United KK-theory combines real, complex, and self-conjugate KK-theory; but unlike unaugmented KK-theory for real C*-algebras, it admits a Universal Coefficient Theorem. For all separable A and B in which the complexification of A is in the bootstrap category, KKCRT(A,B) appears as the middle term of a short exact sequence whose outer terms involve the united K-theory of A and B. As a corollary, we prove that united K-theory classifies KK-equivalence for real C*-algebras whose complexification is in the bootstrap category.