On approximations of groups, group actions, and Hopf algebras.

DOI10.1023/A:1012485910692zbMath1130.20306MaRDI QIDQ5947530

E. I. Gordon, L. Yu. Glebskiĭ, Max A. Alekseyev

Publication date: 16 October 2001

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

group algebrasHopf algebrasbialgebrasapproximability of topological groupsapproximation problemsgroups locally embeddable into the class of finite groupsinvariant meansLEF-groups

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Residual properties and generalizations; residually finite groups (20E26) Local properties of groups (20E25)

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Structure and regularity for subsets of groups with finite VC-dimension ⋮ Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint. ⋮ Combinatorial independence and sofic entropy ⋮ All automorphisms of the Calkin algebra are inner ⋮ Extreme points of the set of density measures ⋮ Approximations of groups, characterizations of sofic groups, and equations over groups ⋮ Stone MV-algebras and strongly complete MV-algebras ⋮ Sofic groups and profinite topology on free groups. ⋮ On approximation of locally compact groups by finite algebraic systems ⋮ Gordon's conjectures 1 and 2: Pontryagin-van Kampen duality in the hyperfinite setting ⋮ On finite sets of small tripling or small alternation in arbitrary groups ⋮ Approximate extension of partial \(\varepsilon\)-characters of Abelian groups to characters with application to integral point lattices.

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