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

Preprint

28 February 2003

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0302335

Abstract

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.

Keywords

UNIVERSAL COEFFICIENT THEOREM
UNITED KK THEORY
ALGEBRAS
CRT

All Related Versions

Version 1, 2003-02-26, ArXiv
Version 2, 2003-02-28, ArXiv

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