
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 |

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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 260; 2019; 186 ppMSC: 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.”
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Table of Contents
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Chapters
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Introduction
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1. Basics
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1. Category Theory
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2. Quasigroups and Loops
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3. Latin Square Designs
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4. Groups with Triality
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2. Equivalence
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5. The Functor ${\mathbf {B}}$
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6. Monics, Covers, and Isogeny in TriGrp
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7. Universals and Adjoints
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8. Moufang Loops and Groups with Triality are Essentially the Same Thing
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9. Moufang Loops and Groups with Triality are Not Exactly the Same Thing
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3. Related Topics
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10. The Functors ${\mathbf {S}}$ and ${\mathbf {M}}$
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11. The Functor ${\mathbf {G}}$
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12. Multiplication Groups and Autotopisms
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13. Doro’s Approach
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14. Normal Structure
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15. Some Related Categories and Objects
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4. Classical Triality
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16. An Introduction to Concrete Triality
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17. Orthogonal Spaces and Groups
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18. Study’s and Cartan’s Triality
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19. Composition Algebras
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20. Freudenthal’s Triality
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21. The Loop of Units in an Octonion Algebra
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Additional Material
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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