A Conjugate System for Twisted Araki-Woods von Neumann Algebras of finite dimensional spaces

2023/04/26 by Yang, Zhiyuan
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2304.13856

Abstract

We compute the conjugate system of twisted Araki-Woods von Neumann algebras L_T(H) for a compatible braided crossing symmetric twist T on a finite dimensional Hilbert space H with norm ‖T‖ <1. This implies that those algebras have finite non-microstates free Fisher information and therefore are always factors of type III_λ (0<λ≤ 1) or II₁ . Moreover, using the nontracial free monotone transport, we show that L_T(H) is isomorphic to the free Araki-Woods algebra L₀(H) when ‖T‖=q is small enough.

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