The radial masa in a free group factor is maximal injective

Official URL: http://dx.doi.org/10.1112/jlms/jdq052

The radial (or Laplacian) masa in a free group factor is the abelian von Neumann algebra generated by the sum of the generators (of the free group) and their inverses. The main result of this paper is that the radial masa is a maximal injective von Neumann subalgebra of a free group factor. We also investigate the tensor products of maximal injective algebras. Given two inclusions B-i subset of M-i of type I von Neumann algebras in finite von Neumann algebras such that each B-i is maximal injective in M-i, we show that the tensor product B-1 circle times B-2 is maximal injective in M-1 circle times M-2 provided at least one of the inclusions satisfies the asymptotic orthogonality property we establish for the radial masa. In particular, it follows that finite tensor products of generator and radial masas will be maximal injective in the corresponding tensor product of free group factors.