<i>C</i>*-Algebras of inverse semigroups

Abstract

There are various algebras which may be associated with a discrete group G . In particular we may consider the complex group ring ℂ G , the convolution Banach algebra l 1 (G), the enveloping C *-algebra C *( G ) of l 1 ( G ), and the reduced C *-algebra determined by the completion of l 1 ( G ) under the left regular representation on l 2 ( G ). There is a substantial literature on the circle of ideas associated with the embeddings