A GENERALIZATION OF THE CUNTZ ALGEBRAS AND MODEL ACTIONS

A Cuntz algebra O(H) is associated functorially with an infinite-dimen sional Hilbert space H. It is a simple C-algebra distinct from the al gebra O(infinity) introduced by Cuntz. Every locally compact group G a cts in a canonical way on O(H), H = L2(G), as a Galois-closed group of automorphisms. The fixed-point subalgebra O(G) together with the rest riction to O(G) of the canonical endomorphism of O(H) provides an abst ract group dual which determines the group. If, furthermore, G is amen able, O(G) and O(H) are isomorphic, a result which is in fact valid fo r finite groups, too. We also consider a generalization involving a Ho pf C-algebra or, more precisely, a regular multiplicative unitary. (C ) 1994 Academic Press, Inc.