Transcription of Noncommutative Geometry Alain Connes
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Noncommutative Geometry Alain Connes
Noncommutative GeometryAlain ConnesContentsPreface6 Introduction71. Measure theory (Chapters I and V)82. Topology andK-theory (Chapter II)143. Cyclic cohomology (Chapter III)194. The quantized calculus (Chapter IV)255. The metric aspect of Noncommutative geometry34 Chapter 1. Noncommutative Spaces and Measure Theory391. Heisenberg and the Noncommutative Algebra of Physical Quantities402. Statistical State of a Macroscopic System and Quantum StatisticalMechanics453. Modular Theory and the Classification of Factors484.
over the center as a direct integral of so-called factors, ... These results thus reduce the understanding of type III factors to that of type II factors and their automorphisms, a task which was completed in the hyperflnite case ... the °ow of weights of the type III fac-tor. This °ow is an invariant of the factor and can, by Krieger’s ...
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