1. Introduction

    1. Philosophical ideas behind von Neumann algebras

    2. Von Neumann, Dirac, and Feynman

  2. Von Neumann algebras

    1. Basic definitions

    2. Basic classification of von Neumann algebras

    3. Non-commutative measure theory and non-commutative topologies and geometries

    4. Modular automorphisms

    5. Joint modular structure and sectors

    6. Basic facts about hyper-finite factors of type III

  3. Braid group, von Neumann algebras, quantum TGD, and formation of bound states

    1. Factors of von Neumann algebras

    2. Sub-factors

    3. II1 factors and the spinor structure of WCW

    4. About possible space-time correlates for the hierarchy of II1 sub-factors

    5. Could binding energy spectra reflect the hierarchy of effective tensor factor dimensions?

    6. Four-color problem,II1 factors, and anyons

  4. Inclusions of II1 and III1 factors

    1. Basic findings about inclusions

    2. The fundamental construction and Temperley-Lieb algebras

    3. Connection with Dynkin diagrams

    4. Indices for the inclusions of type III1 factors

  5. TGD and hyper-finite factors of type II1: ideas and questions

    1. What kind of hyper-finite factors one can imagine in TGD?

    2. Direct sum of HFFs of type II1as a minimal option

    3. Bott periodicity, its generalization, and dimension D=8 as an inherent property of the hyper-finite II1 factor

    4. The interpretation of Jones inclusions in TGD framework

    5. WCW , space-time, and imbedding space and hyper-finite type II1 factors

    6. Quaternions, octonions, and hyper-finite typeII1 factors

    7. Does the hierarchy of infinite primes relate to the hierarchy of II1 factors?

  6. Could HFFs of type II have application in TGD framework?

    1. Problems associated with the physical interpretation of III1 factors

    2. Quantum measurement theory and HFFs of type III

    3. What could one say about II1 automorphism associated with II∞?

    4. What could be the physical interpretation of two kinds of invariants associated with HFFs type III?

    5. Does the time parameter t represent time translation or scaling?

    6. Could HFFs of type III be associated with the dynamics in M4+/-× CP2?

    7. Could the continuation of braidings to homotopies involve Δit?

    8. HFFs of type $III$ as super-structures providing additional uniqueness?

  7. Appendix: Inclusions of hyper-finite factors of type II1

    1. Jones inclusions

    2. Wassermann's inclusion

    3. Generalization from SU(2) to arbitrary compact group