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A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems
 
Siegfried Echterhoff Westfälische Wilhelms-Universität, Münster, Germany
S. Kaliszewski Arizona State University, Tempe, AZ
John Quigg Arizona State University, Tempe, AZ
Iain Raeburn University of Newcastle, Newcastle, NSW, Australia
A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems
eBook ISBN:  978-1-4704-0454-3
Product Code:  MEMO/180/850.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems
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A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems
Siegfried Echterhoff Westfälische Wilhelms-Universität, Münster, Germany
S. Kaliszewski Arizona State University, Tempe, AZ
John Quigg Arizona State University, Tempe, AZ
Iain Raeburn University of Newcastle, Newcastle, NSW, Australia
eBook ISBN:  978-1-4704-0454-3
Product Code:  MEMO/180/850.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1802006; 169 pp
    MSC: Primary 46;

    Imprimitivity 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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Right-Hilbert bimodules
    • 2. The categories
    • 3. The functors
    • 4. The natural equivalences
    • 5. Applications
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1802006; 169 pp
MSC: Primary 46;

Imprimitivity 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.

  • Chapters
  • Introduction
  • 1. Right-Hilbert bimodules
  • 2. The categories
  • 3. The functors
  • 4. The natural equivalences
  • 5. Applications
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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