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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Laplacian MASA in a free group factor


Authors: Allan M. Sinclair and Roger R. Smith
Journal: Trans. Amer. Math. Soc. 355 (2003), 465-475
MSC (2000): Primary 46L10, 46L09
DOI: https://doi.org/10.1090/S0002-9947-02-03173-2
Published electronically: October 9, 2002
MathSciNet review: 1932708
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Abstract: The Laplacian (or radial) masa in a free group factor is generated by the sum of the generators and their inverses. We show that such a masa $\mathcal{B}$is strongly singular and has Popa invariant $\delta(\mathcal{B}) = 1$. This is achieved by proving that the conditional expectation $\mathbb{E} _{\mathcal{B}}$ onto $\mathcal{B}$ is an asymptotic homomorphism. We also obtain similar results for the free product of discrete groups, each of which contains an element of infinite order.


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Additional Information

Allan M. Sinclair
Affiliation: School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland
Email: allan@maths.ed.ac.uk

Roger R. Smith
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: rsmith@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03173-2
Received by editor(s): February 26, 2001
Received by editor(s) in revised form: July 26, 2002
Published electronically: October 9, 2002
Additional Notes: The second author was partially supported by a grant from the National Science Foundation.
Article copyright: © Copyright 2002 American Mathematical Society