Simple infinite-dimensional quotients of the group C★-algebras ofcertain discrete 6-dimensional nilpotent groups

Abstract

We study here the simple infinite-dimensional quotients of the group C *-algebras of two discrete6-dimensional nilpotent groups H 6,1 and H 6,2 as the higher-dimensional analogues of the irrational rotation algebras. P Milnes and S. Walters, jointly and individually, have studied the lower-dimensional cases in a series of papers, and also have started the study of some other 6-dimensional groups. For G = H 6,1 or H 6,2, we can determine the crossed product presentations for the simple quotients of C * ( G), and matrix representations for those arising from non-faithful representations of the groups. The isomorphism classifications of these quotients are obtained using K-theoretic tools, namely, the K-groups and the range of trace on K 0. This marks the first use of K-theory in the classification of quotients for 6-dimensional groups.