On the Modular Theory of von Neumann Algebras

von Neumann algebras;modular automorphism;Pure Mathematics

Boey, Edward

University of Waterloo

关键词: von Neumann algebras;    modular automorphism;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5487/1/Boey_Edward.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The purpose of this thesis is to provide an exposition of the extit{modular theory} of von Neumann algebras.The motivation of the theory is to classify and describe von Neumann algebras which do not admit a trace, and in particular, type III factors.We replace traces with weights, and for a von Neumann algebra $mathcal{M}$ which admits a weight $phi$, we show the existence of an automorphic action $sigma^phi:mathbb{R}ightarrowext{Aut}(mathcal{M})$.After showing the existence of these actions we can discuss the crossed product construction, which will then allow us to study the structure of the algebra.