Amenability of inverse semigroups and their semigroup algebras
John F. R. Duncan, I. Namioka · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1978
Synopsis If G is a group, then G is amenable as a semigroup if and only if l1(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 Es of idempotent elements of S is finite. Some partial results are obtained for inverse semigroups S with infinite Es.