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 | References | Similar Articles | Additional Information

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 is strongly singular and has Popa invariant . This is achieved by proving that the conditional expectation onto 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