Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

C*-Algebras of inverse semigroups

J. Duncana1 and A. L. T. Patersona2

a1 Indiana University and University of Stirling

a2 University of Aberdeen

There are various algebras which may be associated with a discrete group G. In particular we may consider the complex group ring xs2102G, the convolution Banach algebra l1(G), the enveloping C*-algebra C*(G) of l1(G), and the reduced C*-algebra S0013091500003187_inline1 determined by the completion of l1(G) under the left regular representation on l2(G). There is a substantial literature on the circle of ideas associated with the embeddings

S0013091500003187_eqnU1

(Received January 10 1984)