Free products of von Neumann algebras

Source abstract

A new method of constructing factors of type II 1 {\text {II}_1} , called free product, is introduced. It is a generalization of the group construction of factors of type II 1 {\text {II}_1} when the given group is a free product of two groups. If A 1 {A_1} and A 2 {A_2} are two von Neumann algebras with separating cyclic trace vectors and ortho-unitary bases, then the free product A 1 ∗ A 2 {A_1} \ast {A_2} of A 1 {A_1} and A 2 {A_2} is a factor of type II 1 {\text {II}_1} without property Γ \Gamma .