Transition of type in the von Neumann algebras associated to the Connes-Marcolli $GSp_4$-system

Ismail Abouamal

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arXiv · 2403.03932

Transition of type in the von Neumann algebras associated to the Connes-Marcolli $GSp_4$-system

Ismail Abouamal

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Abstract

We study different types of von Neumann algebras arising from the Connes-Marcolli $GSp_4$-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 $I_\infty$ to type $III_1$, with this transition occurring precisely at the inverse temperature $β= 4$.

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Ismail Abouamal. 2024-06-03. Transition of type in the von Neumann algebras associated to the Connes-Marcolli $GSp_4$-system. https://arxiv.org/abs/2403.03932

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