3,668 research outputs found
On Kirchberg's Embedding Problem
Kirchberg's Embedding Problem (KEP) asks whether every separable C
algebra embeds into an ultrapower of the Cuntz algebra . In this
paper, we use model theory to show that this conjecture is equivalent to a
local approximate nuclearity condition that we call the existence of good
nuclear witnesses. In order to prove this result, we study general properties
of existentially closed C algebras. Along the way, we establish a
connection between existentially closed C algebras, the weak expectation
property of Lance, and the local lifting property of Kirchberg. The paper
concludes with a discussion of the model theory of . Several
results in this last section are proven using some technical results concerning
tubular embeddings, a notion first introduced by Jung for studying embeddings
of tracial von Neumann algebras into the ultrapower of the hyperfinite II
factor.Comment: 42 pages; final version to appear in the Journal of Functional
Analysi
On the structural theory of factors of negatively curved groups
Ozawa showed that for any i.c.c., hyperbolic group, the associated group
factor is solid. Developing a new approach that combines some methods of
Peterson, Ozawa and Popa, and Ozawa, we strengthen this result by showing that
these factors are strongly solid. Using our methods in cooperation with a
cocycle superrigidity result of Ioana, we show that profinite actions of
lattices in Sp(n,1), n>1, are virtually W*-superrigid.Comment: Fina version; to appear as such in Annales Scientifiques de l'EN
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