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Moufang Loops and Groups with Triality are Essentially the Same Thing
 
J. I. Hall Michigan State University, East Lansing
Moufang Loops and Groups with Triality are Essentially the Same Thing
Softcover ISBN:  978-1-4704-3622-3
Product Code:  MEMO/260/1252
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5321-3
Product Code:  MEMO/260/1252.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3622-3
eBook: ISBN:  978-1-4704-5321-3
Product Code:  MEMO/260/1252.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
Moufang Loops and Groups with Triality are Essentially the Same Thing
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Moufang Loops and Groups with Triality are Essentially the Same Thing
J. I. Hall Michigan State University, East Lansing
Softcover ISBN:  978-1-4704-3622-3
Product Code:  MEMO/260/1252
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5321-3
Product Code:  MEMO/260/1252.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3622-3
eBook ISBN:  978-1-4704-5321-3
Product Code:  MEMO/260/1252.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2602019; 186 pp
    MSC: Primary 20

    In 1925 Élie Cartan introduced the principal of triality specifically for the Lie groups of type \(D_4\), and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.”

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Basics
    • 1. Category Theory
    • 2. Quasigroups and Loops
    • 3. Latin Square Designs
    • 4. Groups with Triality
    • 2. Equivalence
    • 5. The Functor ${\mathbf {B}}$
    • 6. Monics, Covers, and Isogeny in TriGrp
    • 7. Universals and Adjoints
    • 8. Moufang Loops and Groups with Triality are Essentially the Same Thing
    • 9. Moufang Loops and Groups with Triality are Not Exactly the Same Thing
    • 3. Related Topics
    • 10. The Functors ${\mathbf {S}}$ and ${\mathbf {M}}$
    • 11. The Functor ${\mathbf {G}}$
    • 12. Multiplication Groups and Autotopisms
    • 13. Doro’s Approach
    • 14. Normal Structure
    • 15. Some Related Categories and Objects
    • 4. Classical Triality
    • 16. An Introduction to Concrete Triality
    • 17. Orthogonal Spaces and Groups
    • 18. Study’s and Cartan’s Triality
    • 19. Composition Algebras
    • 20. Freudenthal’s Triality
    • 21. The Loop of Units in an Octonion Algebra
  • 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: 2602019; 186 pp
MSC: Primary 20

In 1925 Élie Cartan introduced the principal of triality specifically for the Lie groups of type \(D_4\), and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.”

  • Chapters
  • Introduction
  • 1. Basics
  • 1. Category Theory
  • 2. Quasigroups and Loops
  • 3. Latin Square Designs
  • 4. Groups with Triality
  • 2. Equivalence
  • 5. The Functor ${\mathbf {B}}$
  • 6. Monics, Covers, and Isogeny in TriGrp
  • 7. Universals and Adjoints
  • 8. Moufang Loops and Groups with Triality are Essentially the Same Thing
  • 9. Moufang Loops and Groups with Triality are Not Exactly the Same Thing
  • 3. Related Topics
  • 10. The Functors ${\mathbf {S}}$ and ${\mathbf {M}}$
  • 11. The Functor ${\mathbf {G}}$
  • 12. Multiplication Groups and Autotopisms
  • 13. Doro’s Approach
  • 14. Normal Structure
  • 15. Some Related Categories and Objects
  • 4. Classical Triality
  • 16. An Introduction to Concrete Triality
  • 17. Orthogonal Spaces and Groups
  • 18. Study’s and Cartan’s Triality
  • 19. Composition Algebras
  • 20. Freudenthal’s Triality
  • 21. The Loop of Units in an Octonion Algebra
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.