Israel Journal of Mathematics

, Volume 168, Issue 1, pp 153–165

On amenability of group algebras, I

Article

DOI: 10.1007/s11856-008-1061-7

Cite this article as:
Bartholdi, L. Isr. J. Math. (2008) 168: 153. doi:10.1007/s11856-008-1061-7

Abstract

We study amenability of algebras and modules (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups.

We show that a group G is amenable if and only if its group ring \( \mathbb{K} \)G is amenable for some (and therefore for any) field \( \mathbb{K} \).

Similarly, a G-set X is amenable if and only if its span \( \mathbb{K} \)X is amenable as a \( \mathbb{K} \)G-module for some (and therefore for any) field \( \mathbb{K} \).

Copyright information

© Hebrew University Magnes Press 2008

Authors and Affiliations

  1. 1.Mathematical InstituteGeorg-August UniversätGöttingenGermany