Proper cocycles and weak forms of amenability

• Autorzy: Paul Jolissaint
• Języki publikacji: EN

Abstrakty

EN

Let G and H be locally compact, second countable groups. Assume that G acts in a measure class preserving way on a standard 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 the sense of Jolissaint (2000) and Knudby (2014). 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. In particular, we show that if Γ and Δ are measure equivalent discrete groups in the sense of Gromov, then such cocycles exist and Γ and Δ share the same weak amenability properties above.

Kategorie tematyczne

• 22D05: General properties and structure of locally compact groups
• 22D10: Unitary representations of locally compact groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 138
• Numer: 1
• Strony: 73-87

Daty

wydano

2015

Twórcy

autor

Paul Jolissaint

• Institut de Mathématiques, Université de Neuchâtel, É.-Argand 11, CH-2000 Neuchâtel, Switzerland

Identyfikatory

DOI

10.4064/cm138-1-5