Real C*-Algebras, United KK-Theory, and the Universal Coefficient Theorem
نویسنده
چکیده
We define united KK-theory for real C*-algebras A and B such that A is separable and B is σ-unital, extending united K-theory in the sense that KKCRT (R, B) = KCRT (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 B is in the bootstrap category, KKCRT (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 KKequivalence for real C*-algebras whose complexification is in the bootstrap category.
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