Vol. 65, No. 1, 1976

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The Cāˆ—-algebras of some real and p-adic solvable groups

Jonathan Rosenberg

Vol. 65 (1976), No. 1, 175ā€“192

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
Received: 2 December 1975
Published: 1 July 1976
Jonathan Rosenberg
Department of Mathematics
University of Maryland
College Park MD 20742-4015
United States