THE PRIMITIVE IDEAL SPACE OF 2-STEP NILPOTENT GROUP-C-ASTERISK ALGEBRAS

Let N be a two-step nilpotent, locally compact, second countable group having center Z and quotient A = N/Z. We study the Jacobson topology on the primitive ideal space Prim C(N) of the group C*-algebra of N. We are able to describe this topology in terms of convergence of subgr oup-representation pairs, as used by the first author in;an earlier wo rk. Under appropriate conditions on N, we are able to describe Prim C (N) globally as the quotient of a principal (A) over cap bundle over ( Z) over cap module an equivalence relation determined entirely by the group structure. We use this second result to compute the primitive id eal spaces of several examples, including all finitely generated, non- torsion two-step nilpotent discrete groups of rank less than or equal to five. Applications of our methods to more general central twisted c rossed products are discussed. (C) 1994 Academic Press, Inc.