MEMO/180/850: A categorical approach to imprimitivity theorems for C*-dynamical systems动力系统非本原法则的专类措施
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作者： S. Kaliszewski 等著
出 版 社：
出版时间： 2006-1-1字数：版次： 1页数： 169印刷时间： 2006/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780821838570包装： 平装内容简介
mprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product $C^*$-algebras. In this work, we show that the Imprimitivity Theorem for induced algebras, Green's Imprimitivity Theorem for actions of groups, and Mansfield's Imprimitivity Theorem for coactions of groups can all be viewed as natural equivalences between various crossed-product functors among certain equivariant categories. The categories involved have $C^*$-algebras with actions or coactions (or both) of a fixed locally compact group $G$ as their objects, and equivariant equivalence classes of right-Hilbert bimodules as their morphisms. Composition is given by the balanced tensor product of bimodules. The functors involved arise from taking crossed products; restricting, inflating, and decomposing actions and coactions; inducing actions; and various combinations of these. Several applications of this categorical approach are also presented, including some intriguing relationships between the Green and Mansfield bimodules, and between restriction and induction of representations.
目录
Introduction
Outline
Epilogue
Chapter 1 Right-Hilbert Bimodules
1.1Right-Hilbert bimodules and partial imprimitivity bimodules
1.2Multiplier bimodules and homomorphisms
1.3Tensor products
1.4The C-multiplier bimodule MC(X C)
1.5Linking algebras
Chapter 2 The Categories
2.1 C*-Algebras
2.2 Group actions
2.3 Group coactions
2.4Actions and coactions
2.5Actions and coactions on linking algebras
2.6Standard factorization of morphisms
2.7Morphisms and induced representations
Chapter 3The Functors
3.1Crossed products
3.2Restriction and inflation
3.3Decomposition
3.4Induced actions
3.5Combined functors
Chapter 4The Natural Equivalences
4.1Statement of the main results
4.2Some further linking algebra techniques
4.3Green's Theorem for induced algebras
4.4Green's Theorem for induced representations
4.5Mansfield's Theorem
Chapter 5Applications
5.1Equivariant triangles
5.2Restriction and induction
5.3Symmetric imprimitivity
Appendix A. Crossed Products by Actions and Coactions
A.1Tensor products
A.2Actions and their crossed products
A.3Coactions
A.4Slice maps and nondegeneracy
A.5Covariant representations and crossed products
A.6Dual actions and decomposition coactions
A.7Normal coactions and normalizations
A.8The duality theorems of Imai-Takai and Katayama
A.9Other definitions of coactions
Appendix B. The Imprimitivity Theorems of Green
and Mansfield
B.1Imprimitivity theorems for actions
B.2Mansfield's imprimitivity bimodule
Appendix C. Function Spaces
C.1The spaces Cc(T, X) for locally convex spaces X
C.2Functions in multiplier algebras and multiplier bimodules
Appendix. Bibliography