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 is a maximal injective von Neumann subalgebra of . When N is equal to infinity, we obtain strongly stable II1 factors (or called McDuff factors) that contain maximal injective abelian von Neumann subalgebras.