Methods of Noncommutative Geometry for Group C'-algebras

Methods of Noncommutative Geometry for Group C'-algebras

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Description

The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form. This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods. The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem.show more

Product details

  • Paperback | 368 pages
  • 156 x 230 x 22mm | 539.78g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 2003.
  • 1584880198
  • 9781584880196

Table of contents

Introduction The Scope and an Example Multidimensional Orbit Methods KK-Theory Invariance IndexC*(G) Deformation Quantization and Cyclic Theories Bibliographical Remarks ELEMENTARY THEORY: AN OVERVIEW BASED ON EXAMPLES Classification of MD-Groups Definitions MD Criteria Classification Theorem Bibliographical Remarks The Structure of C*-Algebras of MD-Groups The C*-Algebra of Aff R The Structure of C*(Aff C) Bibliographical Remarks Classification of MD4-Groups Real Diamond Group and Semi-Direct Products R x H3 Classification Theorem Description of the Co-Adjoint Orbits Measurable MD4-Foliation Bibliographical Remarks The Structure of C*-Algebras of MD4-Foliations C*-Algebras of Measurable Foliations The C*-Algebras of Measurable MD4-Foliations Bibliographic Remarks ADVANCED THEORY: MULTIDIMENSIONAL QUANTIZATION AND INDEX OF GROUP C*-ALGEBRAS Multidimensional Quantization Induced Representation. Mackey Method of Small Subgroups Symplectic Manifolds with Flat Action of Lie Groups Prequantization Polarization Bibliographical Remarks Partially Invariant Holomorphly Induced Representations Holomorphly Induced Representations. Lie Derivative The Irreducible Representations of Nilpotent Lie Groups Representations of Connected Reductive Groups Representations of Almost Algebraic Lie Groups The Trace Formula and the Plancher'el Formula Bibliographical Remarks Reduction, Modification, and Superversion Reduction to the Semi-Simple or Reductive Cases Multidimensional Quantization and U(1)-Covering Globalization over U(1)-Coverings Quantization of Mechanical Systems with Supersymmetry Bibliographical Remarks Index of Type I C*-Algebras Compact Type Ideals in Type I C*-Algebras Canonical Composition series Index of Type I C*-Algebras Application to Lie Group Representations Bibliographical Remarks Invariant Index of Group C*-Algebras The Structure of Group C*-Algebras Construction of IndexC*(G) Reduction of the Indices General Remarks on Computation of Indices Bibliographical Remarksshow more