Structure theory for a class of convolution algebras

Abstract

Introduction* This paper is a chapter in the study of convolution algebras begun in The algebras studied here are algebras of Borel measures on certain compact semigroups, and we describe completely the structure of these algebras. The solution obtained seems remarkable in view of the extreme complexity of the corresponding measure algebras for compact Abelian groups (see Our success is explained by the simple algebraic structure of the semigroups we deal with.