Transition of type in the von Neumann algebras associated to the Connes-Marcolli GSp₄-system

We study different types of von Neumann algebras arising from the Connes-Marcolli GSp₄-system and show that a phase transition occurs at the level of these algebras. More precisely, we show that the type of these algebras transitions from type I_∞ to type III₁, with this transition occurring precisely at the inverse temperature β = 4.