9780821838570

A Categorical Approach to Imprimitivity Theorems for C*-Dynamical Systems

by ; ; ;
  • ISBN13:

    9780821838570

  • ISBN10:

    0821838571

  • Format: Paperback
  • Copyright: 2006-03-01
  • Publisher: Amer Mathematical Society

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Summary

Introduction Right-Hilbert bimodules The categories The functors The natural equivalences Applications Appendix A. Crossed products by actions and coactions Appendix B. The imprimitivity theorems of Green and Mansfield Appendix C. function spaces Appendix. Bibliography

Table of Contents

Introduction 1(2)
Outline 3(3)
Epilogue 6(3)
Right-Hilbert Bimodules
9(24)
Right-Hilbert bimodules and partial imprimitivity bimodules
9(4)
Multiplier bimodules and homomorphisms
13(8)
Tensor products
21(3)
The C-multiplier bimodule MC(X C)
24(3)
Linking algebras
27(6)
The Categories
33(24)
C*-Algebras
33(2)
Group actions
35(2)
Group coactions
37(6)
Actions and coactions
43(1)
Actions and coactions on linking algebras
44(1)
Standard factorization of morphisms
45(6)
Morphisms and induced representations
51(6)
The Functors
57(22)
Crossed products
57(11)
Restriction and inflation
68(3)
Decomposition
71(4)
Induced actions
75(2)
Combined functors
77(2)
The Natural Equivalences
79(22)
Statement of the main results
79(2)
Some further linking algebra techniques
81(5)
Green's Theorem for induced algebras
86(4)
Green's Theorem for induced representations
90(4)
Mansfield's Theorem
94(7)
Applications
101(16)
Equivariant triangles
101(10)
Restriction and induction
111(3)
Symmetric imprimitivity
114(3)
Appendix A. Crossed Products by Actions and Coactions
117(34)
Tensor products
117(4)
Actions and their crossed products
121(5)
Coactions
126(4)
Slice maps and nondegeneracy
130(2)
Covariant representations and crossed products
132(6)
Dual actions and decomposition coactions
138(1)
Normal coactions and normalizations
139(4)
The duality theorems of Imai-Takai and Katayama
143(5)
Other definitions of coactions
148(3)
Appendix B. The Imprimitivity Theorems of Green and Mansfield
151(8)
Imprimitivity theorems for actions
151(4)
Mansfield's imprimitivity bimodule
155(4)
Appendix C. Function Spaces
159(8)
The spaces Cc(T, X) for locally convex spaces X
159(2)
Functions in multiplier algebras and multiplier bimodules
161(6)
Appendix. Bibliography 167

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