Contents
Introduction x i
Lecture 1. von Neumann Algebras 1
1.1. Thre e topologies on 3§{%?) 1
1.2. vo n Neumann's bicommutant theore m 2
1.3. (Concrete ) vo n Neumann algebra s 2
1.4. Factor s 3
1.5. Example s of factors 4
1.6. Compariso n o f projections 6
1.7. Type s I, Hi, Hoc, and II I factors 7
1.8. Standar d for m fo r H i factor s 7
1.9. Th e fundamental grou p of a Hi facto r 8
1.10. Typ e III factors 9
1.11. Hyperfinitenes s 10
Lecture 2. Grou p Actions and Subfactors 13
2.1. Th e coupling constant 13
2.2. Galoi s theory fo r finite group actions 14
2.3. Connes ' results on automorphisms o f R 15
2.4. Extension s o f Connes' automorphism result s 16
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