19 research outputs found
E-Theory for C*-algebras over topological spaces
We define E-theory for separable C*-algebras over second countable
topological spaces and establish its basic properties. This includes an
approximation theorem that relates the E-theory over a general space to the
E-theories over finite approximations to this space. We obtain effective
criteria for determining the invertibility of E-theory elements over possibly
infinite-dimensional spaces. Furthermore, we prove a Universal Multicoefficient
Theorem for C*-algebras over totally disconnected metrisable compact spaces.Comment: 33 page
Nonsplitting in Kirchberg's ideal-related KK-theory
A universal coefficient theorem in the setting of Kirchberg's ideal-related
KK-theory was obtained in the fundamental case of a C*-algebra with one
specified ideal by Bonkat and proved there to split, unnaturally, under certain
conditions. Employing certain K-theoretical information derivable from the
given operator algebras in a way introduced here, we shall demonstrate that
Bonkat's UCT does not split in general. Related methods lead to information on
the complexity of the K-theory which must be used to classify *-isomorphisms
for purely infinite C*-algebras with one non-trivial ideal.Comment: 14 pages, minor typos fixed, 5 figures adde
A Projective C*-Algebra Related to K-Theory
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.Comment: 11 pages. Added a result about the boundary map in K-theor