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Crossed Products by Hecke Pairs
 
Rui Palma University of Oslo, Oslo, Norway
Crossed Products by Hecke Pairs
Softcover ISBN:  978-1-4704-2809-9
Product Code:  MEMO/252/1204
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4377-1
Product Code:  MEMO/252/1204.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2809-9
eBook: ISBN:  978-1-4704-4377-1
Product Code:  MEMO/252/1204.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
Crossed Products by Hecke Pairs
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Crossed Products by Hecke Pairs
Rui Palma University of Oslo, Oslo, Norway
Softcover ISBN:  978-1-4704-2809-9
Product Code:  MEMO/252/1204
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4377-1
Product Code:  MEMO/252/1204.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2809-9
eBook ISBN:  978-1-4704-4377-1
Product Code:  MEMO/252/1204.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2522018; 141 pp
    MSC: Primary 46; Secondary 20

    The author develops a theory of crossed products by actions of Hecke pairs \((G, \Gamma )\), motivated by applications in non-abelian \(C^*\)-duality. His approach gives back the usual crossed product construction whenever \(G / \Gamma \) is a group and retains many of the aspects of crossed products by groups.

    The author starts by laying the \(^*\)-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different \(C^*\)-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminaries
    • 2. Orbit space groupoids and Fell bundles
    • 3. $^*$-Algebraic crossed product by a Hecke pair
    • 4. Direct limits of sectional algebras
    • 5. Reduced $C^*$-crossed products
    • 6. Other completions
    • 7. Stone-Von Neumann Theorem For Hecke Pairs
    • 8. Towards Katayama duality
  • Additional Material
     
     
  • 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: 2522018; 141 pp
MSC: Primary 46; Secondary 20

The author develops a theory of crossed products by actions of Hecke pairs \((G, \Gamma )\), motivated by applications in non-abelian \(C^*\)-duality. His approach gives back the usual crossed product construction whenever \(G / \Gamma \) is a group and retains many of the aspects of crossed products by groups.

The author starts by laying the \(^*\)-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different \(C^*\)-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.

  • Chapters
  • Introduction
  • 1. Preliminaries
  • 2. Orbit space groupoids and Fell bundles
  • 3. $^*$-Algebraic crossed product by a Hecke pair
  • 4. Direct limits of sectional algebras
  • 5. Reduced $C^*$-crossed products
  • 6. Other completions
  • 7. Stone-Von Neumann Theorem For Hecke Pairs
  • 8. Towards Katayama duality
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
Please select which format for which you are requesting permissions.