Mathematics – Operator Algebras
Scientific paper
2007-05-30
Journal of Functional Analysis, Volume 254, Issue 12, 15 June 2008, Pages 3079-3092
Mathematics
Operator Algebras
11 pages. Added a result about the boundary map in K-theory
Scientific paper
10.1016/j.jfa.2008.03.004
The C*-algebra qC is the smallest of the C*-algebras qA introduced by Cuntz in the context of KK-theory. An important property of qC is the natural isomorphism of K0 of D with classes of homomorphism from qC to matrix algebras over D. Our main result concerns the exponential (boundary) map from K0 of a quotient B to K1 of an ideal I. We show if a K0 element is realized as a homomorphism from qC to B then its boundary is realized as a unitary in the unitization of I. The picture we obtain of the exponential map is based on a projective C*-algebra P that is universal for a set of relations slightly weaker than the relations that define qC. A new, shorter proof of the semiprojectivity of qC is described. Smoothing questions related the relations for qC are addressed.
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