About the Connes Embedding Conjecture---Algebraic approaches---

Abstract

This is an expanded lecture note for "Masterclass on sofic groups and applications to operator algebras" (University of Copenhagen, 5-9 November 2012). It is about algebraic aspects of the Connes Embedding Conjecture. It contains new proofs of equivalence of the Connes Embedding Conjecture, Positivstellensatze for trace positive polynomials, Kirchberg's Conjecture, and Tsirelson's Problem.

32 pages; The title is changed and the contents is expanded for publication (v2); Minor changes (v3)

References in corpus (4)

• Connes' embedding problem and Tsirelson's problem
• Connes' embedding conjecture and sums of hermitian squares
• Operator-algebraic superrigidity for $S{L}_n(\mathbb{Z}),n\ge 3$
• The Weak Expectation Property and Riesz Interpolation

Cited by in corpus (8)

• A synchronous game for binary constraint systems
• Algebras, Synchronous Games and Chromatic Numbers of Graphs
• Amenability and uniform Roe algebras
• Correction of a proof in "Connes' embedding conjecture and sums of hermitian squares"
• Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
• Curious properties of free hypergraph C*-algebras
• Independence properties in subalgebras of ultraproduct II${}_1$ factors
• Rigidity for Monogamy-of-Entanglement Games