Proper cocycles and weak forms of amenability

2014/03/02 by Jolissaint, Paul · 2 citations
#22D10 #22D25 #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1403.0207

Abstract

Let G and H be locally compact, second countable groups. Assume that G acts in a measure class preserving way on a standard probability space (X,μ) such that L^∞(X,μ) has an invariant mean and that there is a Borel cocycle α:G× X→ H which is proper in a suitable, natural sense. We show that if H has one of the three properties: Haagerup property (a-T-menability), weak amenability or weak Haagerup property, then so does G. We observe that it is the case for a weak form of measure equivalence for pairs of discrete groups.

Cited by

• Relative solidity results and their applications to computations of some II₁ factor invariants
• Proper cocycles, measure equivalence and L_p-Fourier multipliers

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