Absence of Cartan Subalgebra and Generator Masa is q-Deformed with Approximation Property for q-Araki-Woods Algebras

Abstract

We study some products with mixing subalgebras and non-injectivity with generator Masa of the q-deformed Araki – Woods of von Neumann algebras. We also study a class of II1 factors with at most one Cartan subalgebra II and structure results for free Araki-Woods and their continuous cores. The Q-Gaussian processes, that is, non- commutative and classical aspects with q-deformed Araki- Woods factors are determined. We characterize the asymptotic matricial models, extension of second quantisation, Haagerup approximation property, absence of Cartan subalgebras, the structure of modular invariant subalgrbras and complete metric approximation property for q- Araki- Woods factors and algebras.