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, 71ā€“97

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
Received: 17 March 1976
Revised: 4 April 1977
Published: 1 September 1977
Philip Palmer Green