The Laplacian MASA in a free group factor Academic Article

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 B mathcal {B} is strongly singular and has Popa invariant ( B ) = 1 delta (mathcal {B}) = 1 . This is achieved by proving that the conditional expectation E B mathbb {E}_{mathcal {B}} onto B 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.