Related Experiment Video
Updated: May 13, 2025

Characterization of Anisotropic Leaky Mode Modulators for Holovideo
Published on: March 19, 2016
Operator-Valued Twisted Araki-Woods Algebras
R Rahul Kumar1, Melchior Wirth2,3
1Department of Mathematics and Statistics, IIT Kanpur, Kalyanpur, Uttar Pradesh 208016 India.
Abstract:
We introduce operator-valued twisted Araki-Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes q-Gaussian and q-Araki-Woods algebras and also generalize Shlyakhtenko's von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki-Woods algebras over type factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee the factoriality of these algebras.
Related Concept Videos
Cartesian Vector Notation
SFG Algebra
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
Vector Algebra: Method of Components
In many applications, the magnitudes and directions of...
Radical Anti-Markovnikov Addition to Alkenes: Overview
Vector Algebra: Graphical Method
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Cartesian Form for Vector Formulation

