Modular Theory by example
Operator Algebras
2013-04-12 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
The present article contains a short introduction to Modular Theory for von Neumann algebras with a cyclic and separating vector. It includes the formulation of the central result in this area, the Tomita-Takesaki theorem, and several of its consequences. We illustrate this theory through several elementary examples. We also present more elaborate examples and compute modular objects for a discrete crossed product and for the algebra of canonical anticommutation relations (CAR-algebra) in a Fock representation.
Cite
@article{arxiv.0901.1004,
title = {Modular Theory by example},
author = {Fernando Lledó},
journal= {arXiv preprint arXiv:0901.1004},
year = {2013}
}
Comments
25 pages