Göttingen 2025 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 10: Operator Algebras
MP 10.3: Talk
Thursday, April 3, 2025, 14:50–15:10, ZHG001
Local Structure of Twisted Araki-Woods Algebras — •Ricardo Correa da Silva and Gandalf Lechner — Department of Mathematics, FAU Erlangen-Nürnberg, Erlangen, Germany
Finding models for local nets of von Neumann algebras and understanding the relative commutant M∩N′ for the inclusion N⊂M is a central problem in Algebraic Quantum Field Theory.
In this talk, a family of von Neumann algebras LT(H) with respect to a twist T and a standard subspace H will be introduced and it will be discussed that the Fock vacuum is separating for these algebras if, and only if, the twist T satisfies two physically motivated conditions: crossing-symmetry and the Young-Baxter equation. Furthermore, some properties of the relative commutant of the inclusion LT(K) ⊂LT(H) will be presented.
Keywords: twisted Araki-Woods algebras; algebraic quantum field theory; Tomita-Takesaki modular theory; crossing-symmetry; Yang-Baxter equation