Real C*-algebras, United KK-theory, and the Universal Coefficient Theorem

Details Real C*-algebras, United KK-theory, and the Universal Coefficient Theorem Real C*-algebras, United KK-theory, and the Universal Coefficient Theorem

2003-02-26

arxiv.org/abs/math/0302335v2

Mathematics

Operator Algebras

42 pages; correction to abstract: the correct hypothesis is that the complexification of A (not B) is in the bootstrap categor

Scientific paper

We define united KK-theory for real C*-algebras A and B such that A is separable and B is sigma-unital, extending united K-theory in the sense that KK\crt(\R, B) = K\crt(B). United KK-theory contains real, complex, and self-conjugate KK-theory; but unlike unaugmented real KK-theory, it admits a universal coefficient theorem. For all separable A and B in which the complexification of A is in the bootstrap category, KK\crt(A,B) can be written 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.

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