Sofic representations of amenable groups

DOI10.1090/S0002-9939-2011-11222-XzbMath1263.43001arXiv1010.3424OpenAlexW2087694154MaRDI QIDQ3104450

Gábor Elek, Endre Szabó

Publication date: 13 December 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3424

zbMATH Keywords

amalgamated productsamenable groupssofic groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free probability and free operator algebras (46L54) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (26)

A non-LEA sofic group ⋮ Fuglede-Kadison determinants and sofic entropy ⋮ Metric Approximations of Wreath Products ⋮ A convex structure on sofic embeddings ⋮ On sofic approximations of ⋮ Combinatorial independence and sofic entropy ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ On computing homology gradients over finite fields ⋮ Locally compact sofic groups ⋮ On sofic actions and equivalence relations ⋮ AN INVITATION TO MODEL THEORY AND C*-ALGEBRAS ⋮ An \(l^p\)-version of von Neumann dimension for Banach space representations of sofic groups. II ⋮ Soficity and variations on Higman's group ⋮ Sofic dimension for discrete measured groupoids ⋮ Soficity, short cycles, and the Higman group ⋮ Some closure results for \(\mathcal{C}\)-approximable groups ⋮ Entropy theory for sofic groupoids. I: The foundations ⋮ Convergence theorems for graph sequences ⋮ Independence properties in subalgebras of ultraproduct \(\mathrm{II}_1\) factors ⋮ Constraint metric approximations and equations in groups ⋮ Finitely Presented Groups Related to Kaplansky’s Direct Finiteness Conjecture ⋮ Examples in the entropy theory of countable group actions ⋮ Convex structures revisited ⋮ Factorial relative commutants and the generalized Jung property for \(\mathrm{II}_1\) factors ⋮ Almost commuting permutations are near commuting permutations ⋮ Sofic homological invariants and the Weak Pinsker Property

Cites Work

• The strong approximation conjecture holds for amenable groups
• Amenability, tubularity, and embeddings into \(\mathcal{R}^{\omega}\)
• Hyperlinearity, essentially free actions and \(L^2\)-invariants. The sofic property
• The combinatoral cost
• Free products of sofic groups with amalgamation over monotileably amenable groups
• On sofic groups
• Hyperlinear and Sofic Groups: A Brief Guide

This page was built for publication: Sofic representations of amenable groups