Types of von Neumann Algebras
Year: 2011
Type: dissertation
Abstract: In this thesis we examine the classification theory regarding von Neumann algebras. We will focus on\nthe classification of von Neumann algebras into types, namely type I, II and III. Furthermore the\ndecomposition of von Neumann algebra into a direct integral of factors is included. The classification\nprocess starts with abelian von Neumann algebras. After the abelian von Neumann algebras are classified\nwe examine the general structure of type I and type II von Neumann algebras. We then proceed to\nprovide explicit constructions of factors of the possible types. The focus lies with the general structure\ntheory of von Neumann algebras. Various constructions, such as, the crossed product construction are\nincluded, as it provides us with a tool to construct factors of type II1, type II1 and type III.
Author: Eugene Jacobs
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W344134792