Cuntz semigroups of ideals and quotients and a generalized Kasparov Stabilization Theorem
Operator Algebras
2007-11-01 v1
Abstract
Let A be a C*-algebra and I a closed two-sided ideal of A. We use the Hilbert C*-modules picture of the Cuntz semigroup to investigate the relations between the Cuntz semigroups of I, A and A/I. We obtain a relation on two elements of the Cuntz semigroup of A that characterizes when they are equal in the Cuntz semigroup of A/I. As a corollary, we show that the Cuntz semigroup functor is exact. Replacing the Cuntz equivalence relation of Hilbert modules by their isomorphism, we obtain a generalization of Kasparov's Stabilization theorem.
Keywords
Cite
@article{arxiv.0710.5800,
title = {Cuntz semigroups of ideals and quotients and a generalized Kasparov Stabilization Theorem},
author = {Alin Ciuperca and Leonel Robert and Luis Santiago},
journal= {arXiv preprint arXiv:0710.5800},
year = {2007}
}