Amenability of inverse semigroups and their semigroup algebras

Abstract

Synopsis If G is a group, then G is amenable as a semigroup if and only if l 1 ( G ), the group algebra, is amenable as an algebra. In this note, we investigate the relationship between these two notions of amenability for inverse semigroups S . A complete answer can be given in the case where the set E s of idempotent elements of S is finite. Some partial results are obtained for inverse semigroups S with infinite E s .