Vol. 72, No. 1, 1977

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Cāˆ—-algebras of transformation groups with smooth orbit space

Philip Palmer Green

Vol. 72 (1977), No. 1, 71–97
Abstract

We investigate the structure of certain locally compact Hausdorff transformation groups (G,X) and the C-algebras C(G,X) associated to them. When G and X are second countable and the action is free, we obtain a simple necessary and sufficient condition for C(G,X) to be a continuous trace algebra, and show that the continuous trace algebras so arising are never “twisted” over their spectra. When G is separable compactly generated Abelian and X contains a totally disconnected set of fixed points whose complement, Z, is a trivial G-principal fiber bundle over its orbit space Z∕G, with Z∕G compact, C(G,X) can be described completely using the Brown-Douglas-Fillmore theory of extensions of the compact operators on a separable Hilbert space by a commutative algebra. These results yield as special cases the structure of the C-algebras for several infinite families of solvable locally compact groups.

Mathematical Subject Classification 2000
Primary: 22D25
Secondary: 46L05
Milestones
Received: 17 March 1976
Revised: 4 April 1977
Published: 1 September 1977
Authors
Philip Palmer Green