Amenable actions, free products and a fixed point property

Abstract

We investigate the class of groups admitting an action on a set with an invariant mean. It turns out that many free products admit such an action. We give a complete characterisation of such free products in terms of a strong fixed point property.

12 pages

References in corpus (4)

• Dimension and randomness in groups acting on rooted trees
• On co-amenability for groups and von Neumann algebras
• On some questions of Eymard and Bekka concerning amenability of homogeneous spaces and induced representations
• There is no separable universal II_1-factor

Cited by in corpus (10)

• Isometry groups of non-positively curved spaces: discrete subgroups
• On the topological full group of a minimal Cantor Z^2-system
• Invariant means and the structure of inner amenable groups
• Irreducible lattices, invariant means, and commensurating actions
• Characterizations of locally finite actions of groups on sets
• Furstenberg boundaries for pairs of groups
• Inner amenable groupoids and central sequences
• Realizing residually finite groups as subgroups of branch groups
• Metric approximations of unrestricted wreath products when the acting group is amenable
• Amenable actions of amalgamated free products