Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 55, Number 1 (2011), 205-236.
Fixed-point algebras for proper actions and crossed products by homogeneous spaces
We consider a fixed free and proper action of a locally compact group G on a space T, and actions α : G → Aut A on C∗-algebras for which there is an equivariant embedding of (C0(T), rt) in (M(A), α). A recent theorem of Rieffel implies that α is proper and saturated with respect to the subalgebra Cc(T)ACc(T) of A, so that his general theory of proper actions gives a Morita equivalence between A ⋊α,r G and a generalised fixed-point algebra Aα. Here we investigate the functor (A, α) ↦ Aα and the naturality of Rieffel’s Morita equivalence, focusing in particular on the relationship between the different functors associated to subgroups and quotients. We then use the results to study induced representations for crossed products by coactions of homogeneous spaces G/H of G, which were previously shown by an Huef and Raeburn to be fixed-point algebras for the dual action of H on the crossed product by G.
Illinois J. Math., Volume 55, Number 1 (2011), 205-236.
First available in Project Euclid: 19 December 2012
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an Huef, Astrid; Kaliszewski, S.; Raeburn, Iain; Williams, Dana P. Fixed-point algebras for proper actions and crossed products by homogeneous spaces. Illinois J. Math. 55 (2011), no. 1, 205--236. doi:10.1215/ijm/1355927034. https://projecteuclid.org/euclid.ijm/1355927034