The Laplacian MASA in a free group factor

Sinclair, Allan; Smith, Roger

doi:10.1090/S0002-9947-02-03173-2

The Laplacian MASA in a free group factor
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by Allan M. Sinclair and Roger R. Smith

Trans. Amer. Math. Soc. 355 (2003), 465-475

DOI: https://doi.org/10.1090/S0002-9947-02-03173-2

Published electronically: October 9, 2002

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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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