Linear sofic groups and algebras

DOI10.1090/tran/6706zbMath1406.20038arXiv1212.6780OpenAlexW2964237114MaRDI QIDQ2951903

Liviu Păunescu, Goulnara N. Arzhantseva

Publication date: 10 January 2017

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

Full work available at URL: https://arxiv.org/abs/1212.6780

zbMATH Keywords

linear groupssofic groupsmetric ultraproductKaplansky's direct finiteness conjecture.

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Residual properties and generalizations; residually finite groups (20E26) Ultraproducts and related constructions (03C20) Algebraic geometry over groups; equations over groups (20F70)

Related Items (12)

Metric approximations of unrestricted wreath products when the acting group is amenable ⋮ Metric Approximations of Wreath Products ⋮ Some remarks on finitarily approximable groups ⋮ Infinite dimensional representations of finite dimensional algebras and amenability ⋮ Stable finiteness does not imply linear soficity ⋮ Convergence and limits of linear representations of finite groups ⋮ AN INVITATION TO MODEL THEORY AND C*-ALGEBRAS ⋮ Approximations of groups, characterizations of sofic groups, and equations over groups ⋮ Soficity and hyperlinearity for metric groups ⋮ Almost commuting matrices with respect to the rank metric ⋮ On sofic monoids ⋮ Permanence properties of verbal products and verbal wreath products of groups

Cites Work

• Unnamed Item
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• A sofic group away from amenable groups.
• Exercises in modules and rings.
• Entropy and isoperimetry for linear and non-linear group actions.
• Sofic groups and profinite topology on free groups.
• On amenability of group algebras. I.
• Theory of codes with maximum rank distance
• On tensor products of certain group \(C^*\)-algebras
• Bilinear forms over a finite field, with applications to coding theory
• Endomorphisms of symbolic algebraic varieties
• The amenability of affine algebras
• Sofic groups and direct finiteness.
• On finite approximations of groups and algebras
• \(C^*\)-algebras, Gelfand-Kirillov dimension, and Følner sets
• Maps on matrix and operator algebras
• Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint.
• Product between ultrafilters and applications to the Connes' embedding problem
• A DICHOTOMY FOR THE NUMBER OF ULTRAPOWERS
• Logic for metric structures and the number of universal sofic and hyperlinear groups
• On low rank perturbations of complex matrices and some discrete metric spaces
• On the number of universal sofic groups
• An introduction to hyperlinear and sofic groups
• ON ALGEBRAS THAT HAVE ALMOST FINITE DIMENSIONAL REPRESENTATIONS
• On sofic groups
• Hyperlinear and Sofic Groups: A Brief Guide

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