Vol. 65, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
The Cāˆ—-algebras of some real and p-adic solvable groups

Jonathan Rosenberg

Vol. 65 (1976), No. 1, 175–192
Abstract

When G is a locally compact group, the unitary representation theory of G is the “same” as the -representation theory of the group C-algebra C(G). Hence it is of interest to determine the isomorphism class of C(G) for a wide variety of groups G. Using methods suggested by papers of Z’ep and Delaroche, we determine explicitly the C-algebras of the “ax + b” groups over all nondiscrete locally compact fields and of a number of two-step solvable Lie groups. Only finitely many C-algebras arise as the group C-algebras of 3-dimensional simply connected Lie groups, and we characterize many of them. We also discuss the C-algebras of unipotent p-adic groups.

Mathematical Subject Classification 2000
Primary: 22D25
Secondary: 22E25
Milestones
Received: 2 December 1975
Published: 1 July 1976
Authors
Jonathan Rosenberg
Department of Mathematics
University of Maryland
College Park MD 20742-4015
United States
http://www.math.umd.edu/~jmr