Discrete groups with Kazhdan's property \(T\) and factorization property are residually finite

DOI10.1007/BF01459798zbMath0805.46066MaRDI QIDQ1337521

Eberhard Kirchberg

Publication date: 9 November 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165222

zbMATH Keywords

factorization propertyLie groupproperty (F)residual finitenessnuclearhyperfinite \(\text{II}_ 1\) factordiscrete group with property \(T\) of Kazhdanfaithful unitary representationmaximal almost periodicitytwo-sided regular representation

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Classifications of (C^*)-algebras (46L35)

Related Items (26)

The quantum-to-classical graph homomorphism game ⋮ ABOUT THE QWEP CONJECTURE ⋮ Kazhdan's property T and \(C^{*}\)-algebras ⋮ Invariant states and a conditional fixed point property for affine actions ⋮ About the Connes embedding conjecture ⋮ Approximation properties for noncommutative \(L_p\)-spaces associated with discrete groups ⋮ Faithful actions of automorphism groups of free groups on algebraic varieties ⋮ Amenable traces and Følner \(C^\ast\)-algebras ⋮ Flexible Hilbert-Schmidt stability versus hyperlinearity for property (T) groups ⋮ On locally finite‐dimensional traces ⋮ Amenable representations and finite injective von Neumann algebras ⋮ EXISTENCE OF SPECTRAL GAPS, COVERING MANIFOLDS AND RESIDUALLY FINITE GROUPS ⋮ Subalgebras of simple AF-algebras ⋮ A generalization of expander graphs and local reflexivity of uniform Roe algebras ⋮ Cohomological obstructions to lifting properties for full C*-algebras of property (T) groups ⋮ A synchronous game for binary constraint systems ⋮ Obstructions to matricial stability of discrete groups and almost flat $K$-theory ⋮ Property (T), property (F) and residual finiteness for discrete quantum groups ⋮ A new proof of the Tikuisis-White-Winter theorem ⋮ Topological generation results for free unitary and orthogonal groups ⋮ Kirchberg's factorization property for locally compact groups ⋮ Kirchberg's factorization property for discrete quantum groups ⋮ Hyperlinear and Sofic Groups: A Brief Guide ⋮ A note on commutation relations and finite dimensional approximations ⋮ Property \((T)\) for \(II_ 1\) factors and unitary representations of Kazhdan groups ⋮ On non-semisplit extensions, tensor products and exactness of group \(C^*\)-algebras

Cites Work

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• Erratum to: Topological tensor products and nuclear spaces.
• An elementary account of Selberg's lemma
• \(C^*\)-algebras associated with groups with Kazhdan's property T
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• All reductive \(\mathfrak p\)-adic groups are tame
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Notes on extensions of \(C^*\)-algebras
• On non-semisplit extensions, tensor products and exactness of group \(C^*\)-algebras
• Connection of the dual space of a group with the structure of its closed subgroups
• ON EXACTNESS OF GROUP C^*-ALGEBRASS

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