A Survey on Connes' Embedding Conjecture

Abstract

In a very celebrated paper A. Connes has formulated a conjecture which is now one of the most important open problem in Operator Algebras. This importance comes from the works of many mathematicians who have found some unexpected equivalent statements showing as this conjecture is transversal to almost all the sub-specialization of Operator Algebras. In this survey I would like to give a more or less detailed description of all these approaches.

References in corpus (5)

• Connes' embedding conjecture and sums of hermitian squares
• Invariant means and finite representation theory of C*-algebras
• A Linearization of Connes' Embedding Problem
• There is no separable universal II_1-factor
• A non-commutative, analytic version of Hilbert's 17-th problem in type II${}_1$ von Neumann algebras

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