Illinois Journal of Mathematics

Fixed-point algebras for proper actions and crossed products by homogeneous spaces

Astrid an Huef, S. Kaliszewski, Iain Raeburn, and Dana P. Williams

Full-text: Open access

Abstract

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 Aα,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.

Article information

Source
Illinois J. Math., Volume 55, Number 1 (2011), 205-236.

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1355927034

Digital Object Identifier
doi:10.1215/ijm/1355927034

Mathematical Reviews number (MathSciNet)
MR3006686

Zentralblatt MATH identifier
1261.46063

Subjects
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Citation

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


Export citation