A Projective C*-Algebra Related to K-Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0705.4341,
title = {A Projective C*-Algebra Related to K-Theory},
author = {Terry A. Loring},
journal= {arXiv preprint arXiv:0705.4341},
year = {2008}
}