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Exact large ideals of $ B(G)$ are downward directed


Authors: S. Kaliszewski, Magnus B. Landstad and John Quigg
Journal: Proc. Amer. Math. Soc. 144 (2016), 4401-4412
MSC (2010): Primary 46L55; Secondary 46M15
DOI: https://doi.org/10.1090/proc/13100
Published electronically: April 25, 2016
MathSciNet review: 3531190
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Abstract: We prove that if $ E$ and $ F$ are large ideals of $ B(G)$ for which the associated coaction functors are exact, then the same is true for $ E\cap F$. We also give an example of a coaction functor whose restriction to the maximal coactions does not come from any large ideal.


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Additional Information

S. Kaliszewski
Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287
Email: kaliszewski@asu.edu

Magnus B. Landstad
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Email: magnusla@math.ntnu.no

John Quigg
Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287
Email: quigg@asu.edu

DOI: https://doi.org/10.1090/proc/13100
Keywords: Crossed product, action, coaction, Fourier-Stieltjes algebra, exact sequence, Morita compatible
Received by editor(s): August 17, 2015
Received by editor(s) in revised form: December 21, 2015
Published electronically: April 25, 2016
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 American Mathematical Society