Subhomogeneous AF 𝐶*-algebras and their Fubini products. II

Abstract

If C C is a nuclear C ∗ {C^*} -subalgebra of a C ∗ {C^*} -algebra A A , then we have C ⊗ D = ( A ⊗ D ) ∩ ( C ⊗ B ) C \otimes D = (A \otimes D) \cap (C \otimes B) for any C ∗ {C^*} -algebras B B and D D with D ⊂ B D \subset B . Using this, we show that if A A and B B are AF algebras and A ⊗ F B = A ⊗ B A{ \otimes _F}B = A \otimes B , then either A A or B B must be subhomogeneous.