Kazhdan's property (T) and amenable representations

Bekka, Mohammed E. B.; Valette, Alain

doi:10.1007/bf02571659

Cited by 31 publications

(18 citation statements)

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“…We would like to thank the referee for helpful comments and suggestions that lead to a better presentation of the article, and for informing us that one can use the materials in [4] to obtain (T5) ⇒ (T1) for general countable groups (we only had Proposition 4.3 in the original version.) We would also like to thank Prof. Roger Howe for helpful discussion leading to a simpler argument for Theorem 4.1.…”

Section: Acknowledgementmentioning

confidence: 99%

Spectral Gap Actions and Invariant States

2013

International Mathematics Research Notices

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We define spectral gap actions of discrete groups on von Neumann algebras and study their relations with invariant states. We will show that a finitely generated ICC group Γ is inner amenable if and only if there exist more than one inner invariant states on the group von Neumann algebra L(Γ). Moreover, a countable discrete group Γ has property (T ) if and only if for any action α of Γ on a von Neumann algebra N , every α-invariant state on N is a weak- * -limit of a net of normal α-invariant states.

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Section: Acknowledgementmentioning

confidence: 99%

Spectral Gap Actions and Invariant States

2013

International Mathematics Research Notices

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“…If the action in the conjecture is in fact unitary, then by the result of [3], the representation cannot be amenable in the sense of Bekka. Hence by Proposition 4.2, Zelmanov's conjecture holds for unitary representations.…”

Section: The Construction Of a Non-amenable Skew Fieldmentioning

confidence: 99%

The amenability and non-amenability of skew fields

Elek

2005

Proc. Amer. Math. Soc.

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“…Generalizing the original proof, for example, would require a modification of [10, Proposition 3.2, (T2)] combined with the construction of Vaes [62, Proposition 3.1] that produces, from a unitary co-representation "arising from an orthogonal co-representation", an action on a free Araki-Woods factor preserving the free quasi-free state. [5,Theorem 1], [4,Theorem 2.12.9] generalize to LCQGs? That is, are the following conditions equivalent for a LCQG G?…”

Section: Question 42 Does the Connes-weiss Theoremmentioning

confidence: 99%

Weak mixing for locally compact quantum groups

Viselter¹

2016

Ergod. Th. Dynam. Sys.

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We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the noncommutative Jacobs-de Leeuw-Glicksberg splitting theorem of Runde and the author ["Ergodic theory for quantum semigroups", J. Lond. Math. Soc. (2) 89 (2014) 941-959]. Furthermore, a relation between mixing and weak mixing of state-preserving actions of discrete quantum groups and the properties of certain inclusions of von Neumann algebras, which is known for discrete groups, is demonstrated.Comment: 24 pages; v3: minor changes; to appear in Ergodic Theory and Dynamical System

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Kazhdan's property (T) and amenable representations

Cited by 31 publications

References 10 publications

Spectral Gap Actions and Invariant States

Spectral Gap Actions and Invariant States

The amenability and non-amenability of skew fields

Weak mixing for locally compact quantum groups

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