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

2003/02/26 by Jeffrey L. Boersema, Boersema, Jeffrey L. · 1 citation
Computer Science · Mathematics · #19K35 (Primary) #46L80 #46M18 (Secondary) #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:19K35 #msc:46L80 #msc:46M18

paper · pdf · doi:10.48550/arxiv.math/0302335

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

openalex publication_date 2003/02/26 · arxiv created 2003/02/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Exact sequence between real and complex bivariant K theories and\n application to the Z2 pairing

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