Hyperlinearity, essentially free actions and L2-invariants. The sofic property
By Gábor Elek, Endre Szabó. 2004
192 citations recorded by the source corpus.
Abstract.We prove that Connes’ Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds for sofic groups as well. We introduce the notion of essentially free actions and amenable actions and study their properties.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b69d1e316d37e4e5b9fb35995d0160b3eefe84fe
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In Algebra and Number Theory
In Mathematical Physics
- Russell Lyons
- David J. Aldous
- Valerio Capraro
- Martino Lupini
- Charles Bordenave
- Pietro Caputo
- Tim Austin
- William Slofstra
Citations in the corpus
- Processes on Unimodular Random Networks (2006, background): “…a conjecture of Gottschalk (1973) on “surjunctive” groups in topological dynamics (see Gromov (1999)), the Determinant Conjecture on Fuglede-Kadison determinants (see Elek and Szabó (2005)), and Connes’s (1976) Embedding Conjecture for group von Neumann algebras (see Elek and Szabó (2005)).”
- Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, methodology): “Elek and Szabo in [38] showed that every sofic group is hyperlinear.”