Naturality of symmetric imprimitivity theorems

Astrid An Huef; Steven Kaliszewski; Iain Raeburn; Dana P. Williams

doi:10.1090/S0002-9939-2013-11712-0

Naturality of symmetric imprimitivity theorems

Astrid An Huef, Steven Kaliszewski, Iain Raeburn, Dana P. Williams

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a sub-group. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent and hence have the same representation theory. Here we consider commuting actions of groups H and K on a C*-algebra which are saturated and proper as defined by Rieffel in 1990. Our main result says that the resulting Morita equivalence of crossed products is natural in the sense that it is compatible with homomorphisms and induction processes.

Original language	English (US)
Pages (from-to)	2319-2327
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-2013-11712-0
State	Published - 2013

Keywords

Crossed products
Fixed-point algebras
Naturality
Proper actions on C*-algebras
Symmetric imprimitivity theorem

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AU - Williams, Dana P.

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AB - The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a sub-group. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent and hence have the same representation theory. Here we consider commuting actions of groups H and K on a C*-algebra which are saturated and proper as defined by Rieffel in 1990. Our main result says that the resulting Morita equivalence of crossed products is natural in the sense that it is compatible with homomorphisms and induction processes.

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KW - Fixed-point algebras

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KW - Proper actions on C-algebras

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Naturality of symmetric imprimitivity theorems

Abstract

Keywords

ASJC Scopus subject areas

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