The type III manufactory

2011/01/14 by Palcoux, Sebastien
#46L10 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1101.2827

Abstract

Using unusual objects in the theory of von Neumann algebra, as the chinese game Go or the Conway game of life (generalized on finitely presented groups), we are able to build, by hands, many type III factors.

Related

• On von Neumann's Examples of Types
• The type \rm III₁ factor generated by regular representations of the infinite dimensional nilpotent group B₀^\mathbb Z
• On the two-sided Guionnet-Jones-Shlyakhtenko construction at level three
• Type \rm III₁ factors generated by regular representations of infinite dimensional nilpotent group B₀^{\mathbb N}
• Embedding universality for II₁ factors with property (T)