Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Amenability of inverse semigroups and their semigroup algebras*

J. Duncana1 and I. Namiokaa2

a1 Department of Mathematics, University of Stirling

a2 University of Washington, Seattle, U.S.A.


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.

(Received September 13 1977)


* This paper was assisted in publication by a grant from the Carnegie Trust for the Universities of Scotland.

Work supported by a U.K. S.R.C. Senior Visiting Fellowship.