On Amenability of Group Algebras, I

Abstract

We study amenability of affine algebras (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 KG is amenable for some (and therefore for any) field K.

9 pages, no figure; proof extended from v1, including amenability of modules

Cited by in corpus (6)

• Amenability and uniform Roe algebras
• Amenability of coarse spaces and K-algebras
• Amenability and paradoxicality in semigroups and C*-algebras
• Sylvester rank functions for amenable normal extensions
• Rank-stability of polynomial equations
• A note on commutation relations and finite dimensional approximations