Groupoid normalizers of tensor products

الأصل · EN

We consider an inclusion B M of finite von Neumann algebras satisfying B'∩ M B. A partial isometry v∈ M is called a groupoid normalizer if vBv*, v*Bv B. Given two such inclusions Bᵢ Mᵢ, i=1,2, we find approximations to the groupoid normalizers of B₁ B₂ in M₁ M₂, from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis Bᵢ'∩ Mᵢ Bᵢ, i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries v∈ M satisfying vBv* B and v*v, vv*∈ B.