215 research outputs found
Decomposable approximations of nuclear <i>C</i><sup>*</sup>-algebras
We show that nuclear <i>C</i><sup>*</sup>-algebras have a refined version of the completely
positive approximation property, in which the maps that approximately factorize
through finite dimensional algebras are convex combinations of order zero maps.
We use this to show that a separable nuclear <i>C</i><sup>*</sup>-algebra A which is closely
contained in a <i>C</i><sup>*</sup>-algebra B embeds into B
A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself
We give an example of an exact, stably finite, simple. separable C*-algebra D
which is not isomorphic to its opposite algebra. Moreover, D has the following
additional properties. It is stably finite, approximately divisible, has real
rank zero and stable rank one, has a unique tracial state, and the order on
projections over D is determined by traces. It also absorbs the Jiang-Su
algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also
explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard
order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such
an algebra has been moved to a separate paper (1309.4142 [math.OA]
Relative commutants of strongly self-absorbing C*-algebras
The relative commutant of a strongly self-absorbing
algebra is indistinguishable from its ultrapower . This
applies both to the case when is the hyperfinite II factor and to the
case when it is a strongly self-absorbing C*-algebra. In the latter case we
prove analogous results for and reduced powers
corresponding to other filters on . Examples of algebras with
approximately inner flip and approximately inner half-flip are provided,
showing the optimality of our results. We also prove that strongly
self-absorbing algebras are smoothly classifiable, unlike the algebras with
approximately inner half-flip.Comment: Some minor correction
Locally Trivial W*-Bundles
We prove that a tracially continuous W-bundle over a
compact Hausdorff space with all fibres isomorphic to the hyperfinite
II-factor that is locally trivial already has to be globally
trivial. The proof uses the contractibility of the automorphism group
shown by Popa and Takesaki. There is no
restriction on the covering dimension of .Comment: 20 pages, this version will be published in the International Journal
of Mathematic
Decomposable approximations of nuclear C*-algebras
We show that nuclear C*-algebras have a re ned version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B
Classification of graph C*-algebras with no more than four primitive ideals
We describe the status quo of the classification problem of graph C*-algebras
with four primitive ideals or less
Perturbations of nuclear C*-algebras
Kadison and Kastler introduced a natural metric on the collection of all
C*-subalgebras of the bounded operators on a separable Hilbert space. They
conjectured that sufficiently close algebras are unitarily conjugate. We
establish this conjecture when one algebra is separable and nuclear. We also
consider one-sided versions of these notions, and we obtain embeddings from
certain near inclusions involving separable nuclear C*-algebras. At the end of
the paper we demonstrate how our methods lead to improved characterisations of
some of the types of algebras that are of current interest in the
classification programme.Comment: 45 page
C*-algebras associated with endomorphisms and polymorphisms of compact abelian groups
A surjective endomorphism or, more generally, a polymorphism in the sense of
\cite{SV}, of a compact abelian group induces a transformation of .
We study the C*-algebra generated by this operator together with the algebra of
continuous functions which acts as multiplication operators on .
Under a natural condition on the endo- or polymorphism, this algebra is simple
and can be described by generators and relations. In the case of an
endomorphism it is always purely infinite, while for a polymorphism in the
class we consider, it is either purely infinite or has a unique trace. We prove
a formula allowing to determine the -theory of these algebras and use it to
compute the -groups in a number of interesting examples.Comment: 25 page
Rokhlin Dimension for Flows
This research was supported by GIF Grant 1137/2011, SFB 878 Groups, Geometry and Actions and ERC Grant No. 267079. Part of the research was conducted at the Fields institute during the 2014 thematic program on abstract harmonic analysis, Banach and operator algebras, and at the Mittag–Leffler institute during the 2016 program on Classification of Operator Algebras: Complexity, Rigidity, and Dynamics.Peer reviewedPostprin
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