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Classification of Actions of Discrete Kac Algebras on Injective Factors
 
Toshihiko Masuda Kyushu University, Fukuoka, Japan
Reiji Tomatsu Hokkaido University, Sapporo, Japan
Classification of Actions of Discrete Kac Algebras on Injective Factors
eBook ISBN:  978-1-4704-3609-4
Product Code:  MEMO/245/1160.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Classification of Actions of Discrete Kac Algebras on Injective Factors
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Classification of Actions of Discrete Kac Algebras on Injective Factors
Toshihiko Masuda Kyushu University, Fukuoka, Japan
Reiji Tomatsu Hokkaido University, Sapporo, Japan
eBook ISBN:  978-1-4704-3609-4
Product Code:  MEMO/245/1160.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2452016; 118 pp
    MSC: Primary 46

    The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, the authors show that the Connes–Takesaki module is a complete invariant.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminary
    • 2. Canonical extension of irreducible endomorphisms
    • 3. Kac algebras
    • 4. Classification of modular kernels
    • 5. Classification of actions with non-trivial modular parts
    • 6. Classification of centrally free actions
    • 7. Related problems
    • 8. Appendix
  • 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: 2452016; 118 pp
MSC: Primary 46

The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, the authors show that the Connes–Takesaki module is a complete invariant.

  • Chapters
  • Introduction
  • 1. Preliminary
  • 2. Canonical extension of irreducible endomorphisms
  • 3. Kac algebras
  • 4. Classification of modular kernels
  • 5. Classification of actions with non-trivial modular parts
  • 6. Classification of centrally free actions
  • 7. Related problems
  • 8. Appendix
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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