The split property for inclusions of von Neumann algebras was first introduced by Detlev Buchholz in the study of the AQFT approach to quantum field theory, but has become a much used concept in the mathematical structure theory as well.
Let be two von Neumann algebras with . This inclusion is called split if there is a type I-factor with
M \subseteq F \subseteq N
The inclusion is split iff there exist faithful normal representations of , of such that the map given by
\Phi(mn') := \pi_1(m) \otimes \phi_2(n')
extends to a spatial isomorphism, the tensor product used here is the spatial tensor product.
Definition 5.4.1 und Lemma 5.4.2 in