15 November 2019 Noncommutative boundaries and the ideal structure of reduced crossed products
Matthew Kennedy, Christopher Schafhauser
Duke Math. J. 168(17): 3215-3260 (15 November 2019). DOI: 10.1215/00127094-2019-0032


A C-dynamical system is said to have the ideal separation property if every ideal in the corresponding crossed product arises from an invariant ideal in the C-algebra. In this paper we characterize this property for unital C-dynamical systems over discrete groups. To every C-dynamical system we associate a “twisted” partial C-dynamical system that encodes much of the structure of the action. This system can often be “untwisted,” for example, when the algebra is commutative or when the algebra is prime and a certain specific subgroup has vanishing Mackey obstruction. In this case, we obtain relatively simple necessary and sufficient conditions for the ideal separation property. A key idea is a notion of noncommutative boundary for a C-dynamical system that generalizes Furstenberg’s notion of topological boundary for a group.


Download Citation

Matthew Kennedy. Christopher Schafhauser. "Noncommutative boundaries and the ideal structure of reduced crossed products." Duke Math. J. 168 (17) 3215 - 3260, 15 November 2019. https://doi.org/10.1215/00127094-2019-0032


Received: 7 November 2017; Revised: 2 June 2019; Published: 15 November 2019
First available in Project Euclid: 30 October 2019

zbMATH: 07154925
MathSciNet: MR4030364
Digital Object Identifier: 10.1215/00127094-2019-0032

Primary: 46L35
Secondary: ‎43A65 , 45L55 , 47L65

Keywords: C$^{*}$-dynamical system , ideal structure , noncommutative boundary , reduced crossed product

Rights: Copyright © 2019 Duke University Press


This article is only available to subscribers.
It is not available for individual sale.

Vol.168 • No. 17 • 15 November 2019
Back to Top