ABOUT THE QWEP CONJECTURE

By Nathanial P. Brown Narutaka Ozawa. 2003

137 citations recorded by the source corpus.

This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f7b36d8ab2fa0fbc94adf35e1896de1536629d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Grothendieck's Theorem, past and present (2011, background): “We refer the reader to [110] for an excellent exposition of this topic.”
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “We refer to the original paper by Kirchberg [77] and to the more recent survey by Ozawa [90] for the proof of this theorem.”
Hyperlinearity, essentially free actions and L2-invariants. The sofic property (2004, background): “In [12] Ozawa showed that the groups with factorization property are closed when taking subgroups, extensions by amenable quotients, free products, and increasing union (like sofic groups).”
A Linearization of Connes' Embedding Problem (2007, unknown): “O A ] 2 6 Ju n 20 07”
Operator system quotients of matrix algebras and their tensor products (2011, unknown): “e a further extension, replacing C∗(F∞) with a free product of C∗-algebras Ai in which each of the maps idA i is locally liftable. An exposition of the results of Kirchberg and Pisier can be found in [13]. One of our main results in this paper is a new proof of Kirchberg’s theorem (see Corollary 3.2”
Model theory of operator algebras III: elementary equivalence and II1 factors (2011, background): “See [43] for a survey of its equivalents in operator algebras, and [44] for an exposition of its relation to hyperlinear and sofic groups.”
Sofic equivalence relations (2009, background): “Therefore it is enough to construct (see [10]) unital maps ψn : Fθ → Matin×in(C) for some sequence of integers {in} ∞ n=1 such that for each K,L ∈ Fθ the following conditions are satisfied.”
Noncommutative $L^{p}$-spaces without the completely bounded approximation property (2010, background): “This is related to Connes’ embedding problem (which is equivalent to the QWEP conjecture, see [22] for a survey).”
Tensor Products of C*-Algebras and Operator Spaces (2020, methodology): “72 is easy to deduce from Ozawa’s viewpoint in [189], but apparently was not formulated yet.”
FINITARY APPROXIMATIONS OF GROUPS AND THEIR APPLICATIONS (2017, result): “Is the class of Frobenius-approximated groups closed under central quotients or crossed products byZ, compare with Ozawa, Rørdam, and Sato [2015] and Thom [2010]?”
Connes' embedding problem and Tsirelson's problem (2010, background): “That this is indeed a reformulation of Connes’ embedding problem is a deep result of Kirchberg [16, 20].”
Characterisations of the weak expectation property (2013, background): “There are alternate proofs for the assertion that C(Fn) has LP: see [23, 28], for example.”
COMBINATORIAL ASPECTS OF CONNES'S EMBEDDING CONJECTURE AND ASYMPTOTIC DISTRIBUTION OF TRACES OF PRODUCTS OF UNITARIES (2004, background): “embeddingconjectureforthe caseof discretegroupsstates thateverydiscrete group Γ can be asymptotically embedded in the algebra of N by N matrices, when N tends to inﬁnity. As observed in [9] (see also [6] and [4]) it a mounts to prove that for every ﬁnite subset F of Γ, for every ε > 0, there exis”
About the Connes Embedding Conjecture---Algebraic approaches--- (2012, background): “ned by θ(a) = ϕ(1)∗ϕ(a) is a positive contraction from Ainto M, which sends unitary elements to unitary elements and preserves the tracial state. By a multiplicative domain argument (Corollary 2.6 in [Oz1]), the map θis a Jordan morphism. Thus, there is a central projection pin θ(A)′′ such that pθ(r”