About the Connes embedding conjecture

By Nathanial P. Brown Narutaka Ozawa. 2013

144 citations recorded by the source corpus.

In his celebrated paper in 1976, A. Connes casually remarked that any finite von Neumann algebra ought to be embedded into an ultraproduct of matrix algebras, which is now known as the Connes embedding conjecture or problem. This conjecture became one of the central open problems in the field of operator algebras since E. Kirchberg’s seminal work in 1993 that proves it is equivalent to a variety of other seemingly totally unrelated but important conjectures in the field. Since then, many more equivalents of the conjecture have been found, also in some other branches of mathematics such as noncommutative real algebraic geometry and quantum information theory. In this note, we present a survey of this conjecture with a focus on the algebraic aspects of it.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3d51cf7080ba925cbdbdd30a2cde0c2b6b175591

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Citations in the corpus

Characterisations of the weak expectation property (2013, result): “This result can also be found in Ozawa [24].”
THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED (2017, background): “I thank Jason Crann, Richard Cleve, Tobias Fritz, Li Liu, Martino Lupini, Narutaka Ozawa, Vern Paulsen, Mark Sapir, Jamie Sikora, and Thomas Vidick for helpful comments and conversations.”
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The surveys [90, 93, 92] contain several other equivalent reformulations of the Connes’ embedding conjecture in purely algebraic or C*-algebraic terms.”