Maximal injective subalgebras of tensor products of free group factors

In this article, we prove the following results. Let L(F(ni )) be the free group factor on ni generators (ni 2) and λ(gi ) be one of standard generators of L(F(ni )) for 1 i N. Let Ai be the abelian von Neumann subalgebra of L(F(ni )) generated by λ(gi ). Then the abelian von Neumann subalgebra N i=1Ai is a maximal injective von Neumann subalgebra of N i=1 L(F(ni )). When N is equal to infinity, we obtain strongly stable II1 factors (or called McDuff factors) that contain maximal injective abelian von Neumann subalgebras. © 2006 Elsevier Inc. All rights reserved.